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┌──────────────────────────────────────────────────────────────────────────┐ │ HOP - FRACTALS IN MOTION Version 1.2 / 1994 │ ├──────────────────────────────────────────────────────────────────────────┤ │ Copyright (c)1994 by Michael Peters & Randall Scott. All Rights Reserved │ └──────────────────────────────────────────────────────────────────────────┘ HOP is a fractal generator for IBM compatible PCs. If you're not sure what a fractal generator is, never mind. Let's say, HOP creates pretty pictures based on a special kind of mathematical formula. HOP comes with two independent programs: an interactive version that can be used to design new fractals, images and animations, read and write HOP parameter files and GIF image files a non-interactive screensaver version HOP is a DOS program, but both the interactive version and the screensaver can also be used under Microsoft Windows or IBM OS/2. HOP is distributed as shareware. If you like the program and continue using it, you are invited to become a registered user. Registered versions contain some additional features (see chapter 'Registering'). Please give unregistered versions of HOP to your friends. ────────────────────────── To start with HOP, do the following: 1. Install the program on your harddisk, as described in the 'Installation' chapter 2. Configure HOP for your video hardware, as described under 'Video Installation' 3. Run the demo to see what HOP can do (takes 20 minutes on a 486/33) 4. Start to experiment with HOP, as described under 'Quick Start' 5. Read the 'Tutorial' chapter (see Appendix D) and learn how to use HOP ┌────────────────────────────────────────────────────────────────────────┐ │ UPGRADE NOTICE │ └────────────────────────────────────────────────────────────────────────┘ If you have an earlier version of HOP, install the new version over the old version. If you have registered HOP, enter HOP REGISTER to enter your registration number. If you have lost it, contact one of the authors; we'll be glad to help you. ===================== HOP - Fractals in Motion ================= Page 2 ┌────────────────────────────────────────────────────────────────────────┐ │ CONTENTS │ └────────────────────────────────────────────────────────────────────────┘ Revision History . . . . . . . . . . . . . . . . . . . . . . . . 3 Hardware Requirements . . . . . . . . . . . . . . . . . . . . . . 3 Operating Systems . . . . . . . . . . . . . . . . . . . . . . . . 3 File List . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Video Installation . . . . . . . . . . . . . . . . . . . . . . . 6 Installation for Microsoft Windows or IBM OS/2 . . . . . . . . . 7 Quick Start . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The Screensaver Module (HOPSVR.EXE) . . . . . . . . . . . . . . . 9 What Does "HOP" Mean Anyway ? . . . . . . . . . . . . . . . . . . 12 The Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . 13 The User Interface . . . . . . . . . . . . . . . . . . . . . . . 15 Page 1: Fractal Values . . . . . . . . . . . . . . . . . . . . 17 Page 2: Math Effects . . . . . . . . . . . . . . . . . . . . . 21 Page 3: Graphic Effects . . . . . . . . . . . . . . . . . . . . 24 Page 4: Colors . . . . . . . . . . . . . . . . . . . . . . . . 32 HOP's Palette Editor . . . . . . . . . . . . . . . . . . . . . 36 Page 5: Tuning HOP . . . . . . . . . . . . . . . . . . . . . . 38 Page 6: Configuration . . . . . . . . . . . . . . . . . . . . . 41 Page 7: Read File . . . . . . . . . . . . . . . . . . . . . . . 44 Page 8: Save File . . . . . . . . . . . . . . . . . . . . . . . 46 Generate Animation Parameters . . . . . . . . . . . . . . . . . 48 Hotkey List . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Command Line Parameters . . . . . . . . . . . . . . . . . . . . . 54 Troubleshooting / Frequently Asked Questions . . . . . . . . . . 56 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Registering . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Support / Contact . . . . . . . . . . . . . . . . . . . . . . . . 61 Copyrights . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Related Products . . . . . . . . . . . . . . . . . . . . . . . . 63 Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Appendix A: Configuration file HOP.INI . . . . . . . . . . . . . 65 Appendix B: *.HOP parameter set files . . . . . . . . . . . . . . 67 Appendix C: The Hopalong algorithm . . . . . . . . . . . . . . . . 69 Appendix D: Tutorial . . . . . . . . . . . . . . . . . . . . . . . 71 Appendix E: Wish List . . . . . . . . . . . . . . . . . . . . . . 76 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 ===================== HOP - Fractals in Motion ================= Page 3 ┌────────────────────────────────────────────────────────────────────────┐ │ REVISION HISTORY │ └────────────────────────────────────────────────────────────────────────┘ 1.0 8-94 Initial version 1.1 10-94 minor bug fixes (and changed rotation hotkeys) 1.2 11-94 more minor bug fixes (and changed Internet/CIS addresses) ┌────────────────────────────────────────────────────────────────────────┐ │ HARDWARE REQUIREMENTS │ └────────────────────────────────────────────────────────────────────────┘ A SuperVGA adapter/screen is strongly recommended. (HOP does run with 16-color EGA or standard VGA but this won't look very impressive.) A mathematical coprocessor is also strongly recommended. (HOP can run without a coprocessor, but the overall speed will be very unsatisfactory compared to the speed of a 486/33 which is the computer type that the demo was designed on.) You need about 490k free memory space to run HOP. ┌────────────────────────────────────────────────────────────────────────┐ │ OPERATING SYSTEMS (MS-DOS, Microsoft Windows, IBM OS/2) │ └────────────────────────────────────────────────────────────────────────┘ HOP is a DOS program. If you prefer using a modern operating system like Microsoft Windows or IBM OS/2, this shouldn't keep you from enjoying HOP because both of these support DOS applications. HOP runs happily in a DOS session under Windows or OS/2 ! Before installing HOP for Windows or OS/2, you must have installed it for DOS as described on page 5 ff. Then after a successful DOS installation you can install a Windows or OS/2 program icon for the interactive version of HOP as described in the installation chapter on page 7. You can also use HOP's screensaver feature for Windows and for OS/2. The Windows screensaver functionality is already contained in the HOP package you received. If you run OS/2, you need an additional screensaver shell which is available as shareware. Refer to the screensaver chapter (page 9 ff.) for details on the installation of a HOP screensaver under Windows or OS/2. Sounds complicated? Just follow the instructions on the next pages. ===================== HOP - Fractals in Motion ================= Page 4 ┌────────────────────────────────────────────────────────────────────────┐ │ FILE LIST │ └────────────────────────────────────────────────────────────────────────┘ Please give unregistered copies of HOP to others, but if you do, be sure to keep the following files together (or just distribute the packed file HOPZIP.EXE that contains everything): HOP.EXE: the interactive fractal generator HOP.OVR: overlay file belonging to HOP.EXE HOP.DOC: this text file DEMO.HOP: a collection of images/animations that show what HOP can do DEMO.BAT: a batch file to start the demo HOPSAVER.BAT: a batch file to start the screensaver HOPTSR.EXE: the screensaver shell HOPSVR.EXE: the HOP screensaver module HOPSVR.SCR: Windows screensaver management file HOPSVR.PIF: Windows PIF file for the HOP screensaver module Caution: HOP.INI is not supposed to be given to other users because it contains video (and other) configuration data that are specific for each PC (see below). HOP will refuse to run if files are missing (this also applies to the screensaver). All files that belong to HOP should be put into one directory, except for HOPSVR.SCR and HOPSVR.PIF which belong in the Windows directory. We ask you to leave HOP's files completely unaltered, i.e. please don't edit this DOC file or the DEMO.HOP collection. Of course you can add parameter files with your own masterpieces when you give HOP to your friends. ───────────────── If you received a file called HOP.INI (HOP's configuration file from another PC) along with the above listed files, HOP will inform you during installation that it found an invalid configuration and ask if you want to reconfigure HOP. Invalid configuration data can lead to errors and unexpected behaviour, so please answer 'yes'. The same will happen if you transfer your installed HOP files to another harddisk. If this harddisk is on the same computer, you don't need to reconfigure. ===================== HOP - Fractals in Motion ================= Page 5 ┌────────────────────────────────────────────────────────────────────────┐ │ INSTALLATION │ └────────────────────────────────────────────────────────────────────────┘ HOP can be used from Windows or OS/2, but it has to be installed from DOS (or from a DOS session) first, so be sure to see a DOS prompt C:\> before you continue. - Make a 'HOP' directory on your harddisk: MD \HOP - Change into the new directory: CD \HOP - Unpack the file HOPZIP.EXE that contains HOP into the new directory: A:HOPZIP - else: if you received unpacked files instead of a packed file HOPZIP, just copy them into the new directory. (You don't have to change DOS paths or settings.) COPY A:*.* If you have received a HOP.INI configuration file along with the other files, you should delete it to avoid potential problems before continuing: ERASE HOP.INI - If you have Microsoft Windows, copy 2 of the files to your Windows directory: COPY HOPSVR.PIF C:\WINDOWS COPY HOPSVR.SCR C:\WINDOWS - Look up the command line syntax: HOP /? - Start the program to configure the available video modes: HOP - Then restart the program in 'improvising' mode: HOP or rather start the demo to see what HOP can do: DEMO (or HOP DEMO) - If you want a printed manual, copy it to your printer by typing COPY HOP.DOC PRN: If HOP finds no coprocessor, there will be a message after the logo. HOP does run on systems without a coprocessor, but unless you have a 486SX or above, it will run too slowly for good results. If you have moved the files HOPSVR.PIF and HOPSVR.SCR to your Windows directory, HOP may ask you to enter the name of the Windows directory. If HOP cannot find these two files, it refuses to run. ===================== HOP - Fractals in Motion ================= Page 6 ┌────────────────────────────────────────────────────────────────────────┐ │ VIDEO INSTALLATION │ └────────────────────────────────────────────────────────────────────────┘ When starting for the first time, HOP must be configured for your video hardware. This will take a minute, but it is a prerequisite for successful functioning. The only video standard covering SuperVGA resolutions is called VESA (Video Engineers Standard Association). Either your video hardware follows the VESA standard, or it doesn't. If the hardware is not VESA compatible, you can also load a memory resident VESA driver (which is a piece of software you can get from your hardware dealer) to make it VESA compatible. HOP will run without problems if it finds VESA compatibility. It will also run on video hardware that is not VESA compatible, but there are dozens of different video hardware types (each of them different), and there is a chance that your hardware doesn't belong to the types that are supported by HOP. If your PC is capable of high display resolutions, but HOP works with low resolutions only, finding a VESA driver is the remedy. There are up to eight different resolutions (or 'video modes') that HOP can display. 'Video modes' differ in screen resolution (measured in horizontal and vertical number of pixels that are displayed) and the number of colors that an image can contain (usually this is 256). Most video cards can run in several video modes (higher resolutions can only be displayed if the video card is equipped with enough memory chips). The modes are alternative ways to display an image - the higher the resolution, the better the resulting image will usually look. A resolution of 640 * 480 pixels looks good enough for most purposes. Each of the 8 possible resolutions has to be tested during the installation procedure because every combination of video card, driver, and screen will result in a different set of working video modes. The test has to be done by you, because in some cases the computer can't detect if the video mode produces an image or just garble. HOP will store the test results in its configuration file. The available video modes will then be contained in a menu and can be accessed anytime. To test a video mode, you only have to press the key that corresponds to the mode number (0-7). Each time, HOP will leave the text mode screen and try to display a graphics mode message. One of 3 things will happen then: - A 'Press Enter if you can read this' message indicates that this particular mode worked. Be patient - it may take a second or two until this message appears ! Press Enter and continue with the next video mode if the screen looks ok. ===================== HOP - Fractals in Motion ================= Page 7 - If you see the message 'Press Esc if you can read this', this particular video mode didn't work. Press the Esc key and continue with the next video mode. - If the message appears to be garbled, or no message is visible at all, press the Esc key to disable this particular video mode. If only one or two video modes were found to work after completion of the test, this indicates that the current hardware is not supported by HOP unless you make it VESA compatible. After checking the 8 video modes, HOP will store the results in a comfiguration file and return to the operating system. Restart HOP by typing HOP, or watch the demo (type DEMO or HOP DEMO). HOP will start running under the highest resolution found to work. You can change the current resolution anytime by pressing m or M, or by choosing a resolution from a menu. If your hardware situation changes (or if you install a VESA driver), you should rerun the video installation. This can also be done from the menu (see below) or by simply deleting the HOP.INI configuration file. HOP will now either start to improvise, or play back a .HOP parameter file (e.g. if you started the DEMO batch file). ┌────────────────────────────────────────────────────────────────────────┐ │ INSTALLATION FOR MICROSOFT WINDOWS or IBM OS/2 │ └────────────────────────────────────────────────────────────────────────┘ After the complete DOS installation and video configuration, HOP can also be installed for Windows or OS/2. Under all of these operating systems, HOP can either be run interactively or as a screensaver. Read the Screensaver chapter for information on how to install HOP as screensaver for Windows or OS/2. To install a program object for the *interactive* version, follow these steps: Microsoft Windows - From the Program Manager menu, choose 'New' and 'Program'. Enter: Description : HOP Command Line : C:\HOP\HOP.EXE Work Directory : C:\HOP IBM OS/2 - Open the Command Prompts folder, right-click on the DOS fullscreen icon and copy it (new name: HOP) to the Desktop - Right-click on the new object, open the settings, and enter: Path and file name : C:\HOP\HOP.EXE Working Directory : C:\HOP - On the 'Session' page, choose 'DOS fullscreen'. You can also create a program group / folder for HOP, put your new HOP icon into it, and create an additional icon for the demo. (Adding 'DEMO' on the parameter line will cause HOP to run the demo.) ===================== HOP - Fractals in Motion ================= Page 8 ┌────────────────────────────────────────────────────────────────────────┐ │ QUICK START │ └────────────────────────────────────────────────────────────────────────┘ In the beginning you need to know just a few hotkeys. If you are very impatient and don't want to continue reading the manual, this is all you need to know right now. To really understand what happens, you should continue reading the next chapters, especially 'Basic Concept'. Load the DEMO parameter file by issuing HOP DEMO on the command line, or just run HOP without parameters to start it in 'improvising' mode. Esc stops the program anytime. Space Bar skips the current fractal and starts a new one. Ins keeps the current fractal until you press the space bar. F1 displays the keyboard hotkey layout. Enter switches to the user interface from which you can configure HOP, read and write files, and modify all parameters. If you press HELP from the user interface, there will be context sensitive help for every item as well as general information. p, P, alt-p load different color algorithms. f, F loads the next/previous formula. * assigns different random values to the formula constants, changing the shape of the fractal. alt-t switches the 'Transform' effect on and assigns a random value to the transform constant, changing the shape of the fractal. Press ctrl-t to switch 'Transform' off. x changes the shape of the pixels being drawn. There are almost a dozen pixel shapes. i, I increases/decreases pixel size (this works with most pixel shapes). Everything will run much faster with small pixels, but the bigger they are, the more their shapes will influence the look of the fractal. ║ As soon as you press one of the hotkeys that affects the image, the ║ ║ current image will be kept and not be replaced by another image. (You ║ ║ can also press the Ins key to make the current image stay if you like ║ ║ it.) Now the current fractal can be tailored until it is good enough ║ ║ for storing in a HOP parameter file (press s to save to a file). ║ ║ When you are tired of the current image, press the space bar and a ║ ║ new image will come up. ║ There are many more hotkeys. They will be explained in the next chapters. ===================== HOP - Fractals in Motion ================= Page 9 ┌────────────────────────────────────────────────────────────────────────┐ │ THE SCREENSAVER MODULE (HOPSVR.EXE) │ └────────────────────────────────────────────────────────────────────────┘ Interactive Version (HOP.EXE) vs. Screensaver (HOPSVR.EXE) ────────────────────────────────────────────────────────── To save memory space, the HOP screensaver module is a program of its own. It has no user interface; it can't display GIF images. It can, however, playback .HOP parameter files, and there is even one hotkey: if you press s (save), the parameters of the current image are saved to HOPSVR.HOP and can later be edited using HOP. Most of this documentation refers to the interactive version of HOP (HOP.EXE). The screensaver version (HOPSVR.EXE) cannot be interacted with while it runs (except for the 's' parameter saving feature). The screensaver files need to be located in the HOP directory and must be accompanied by all other files belonging to HOP. Before running the screensaver, you must have installed HOP and passed the initial video test. The screensaver needs the HOP.INI configuration file. Operating Systems ───────────────── You can use HOP as a screensaver. HOP's "natural habitat" is DOS, so the screensaver was written for DOS, but it can also be used for DOS sessions under Microsoft Windows and OS/2. The Windows functionality is already contained in the HOP package - see below. To run HOPSVR.EXE as a screensaver for OS/2, you need an OS/2 screensaver shell that can run DOS programs. We recommend 'ScreenSaver' by Siegfried Hanisch in combination with Olaf Koch's ScreenSaver module 'EXTERNAL'. You will find the latest version of 'ScreenSaver' on CompuServe in the OS2USER forum in library 4 or on the Internet FTP archive ftp.cdrom.com in the pub/os2/2_x/graphics directory. Olaf Koch's module 'EXTERNAL' is part of his package of modules for 'ScreenSaver', distributed as SSOK.ZIP. It is usually located at the same places as 'ScreenSaver'. The latest version of 'ScreenSaver' known at the time of writing is 1.5. Andy Cramer's HOPTSR ──────────────────── The HOP screensaver uses a program called HOPTSR (Copyright see below). HOPTSR was developed and customized for HOP by Andrew Cramer. (Thanks to Andy for allowing us to use his program!) HOPTSR is a screensaver 'shell' that waits for a specified time of inactivity, then runs the program that was issued on the command line (default is HOPSVR.EXE, the screensaver module of HOP). HOPSVR.SCR and HOPSVR.PIF are needed if you want to run the screensaver under Microsoft Windows. ===================== HOP - Fractals in Motion ================= Page 10 HOPTSR.EXE, HOPSVR.SCR and HOPSVR.PIF are licensed from Andrew Cramer for the benefit of users running HOP products for personal use. As you can see, his approach to making a DOS program into a ScreenSaver is quite novel. A small version of his ScreenSaver Kit (260K) is available as Shareware on CompuServe (Go GRAPHVEN - Lib #3 - SCRSVR.EXE) or America OnLine under Top Picks in the DOS Software Section. The kit allows the user to transform any DOS program into a ScreenSaver for DOS/Windows and OS/2 DOS boxes. It contains several customizable user modules and extensive documentation. The larger Registered Version is available for $18 from him at P.O. Box 114, Mountain Lakes, NJ 07046 US. Credit Card payment can be online on CompuServe GO SWREG (SCRSVR.EXE). For direct orders, Andy asks that you send only US funds and that foreign orders add $5.00 for shipping and handling. Andy can be reached on CompuServe at 70670,3620 InterNet aic@world.std.com AOL AndYIC Voice and Fax (201)316-0750 Starting the Screensaver from DOS ───────────────────────────────── Enter HOPSAVER (or HOPTSR) to load the memory resident HOPTSR.EXE. (HOPSAVER.BAT starts HOPTSR.EXE with certain parameters, see below) Enter HOPTSR /U to unload it from memory. If you want the HOP screensaver to run every time you use your computer, just add the following lines to your AUTOEXEC.BAT: CD \HOP CALL HOPSAVER.BAT HOPTSR Parameters ───────────────── The full command line syntax of HOPTSR (the screensaver shell for HOP) can be displayed by typing HOPTSR /?. Parameters that you should know are: The /N parameter allows NEW parameters to be passed to an already loaded HOPTSR, and also may be present for initial loading. The /T parameter specifies the inactivity time after which the program will become active. The /C parameter means that all following parameters will be transferred to the program. The /W parameter disables a HOP screensaver that was loaded under DOS when running under Windows (it does not disable the HOP screensaver for Windows). This prevents potential problems that might occur with certain combinations of mouse drivers and the screensaver. HOPSAVER.BAT is a batch file that basically looks like this: @HOPTSR /N /W /T3:00 /Cdemo.hop /randomplay ===================== HOP - Fractals in Motion ================= Page 11 This means that after loading, the HOPTSR program will wait for 3 minutes of inactivity. If 3 minutes pass without a key pressed, the current memory contents will be saved to harddisk and HOPSVR, the screensaver module of HOP, will be loaded, playing parameter sets of the demo (in random order) until you press a key. To activate the screensaver manually use ctrl-leftshift-S. You can modify the batch file to let the HOP screensaver run in improvising mode (i.e. without any /C parameters) or play back parameter files. How to install the Screensaver for Microsoft Windows ──────────────────────────────────────────────────── - Copy HOPSVR.SCR and HOPSVR.PIF into your Windows directory. - If you put HOP into a directory other than C:\HOP, use the Windows PIF Editor to edit HOPSVR.PIF. Change the work directory entry accordingly. - Click on SYSTEM and DESKTOP, then choose 'HOP Screensaver' from the list of available screensavers. - If you want to run the DEMO.HOP collection (or other parameter files) as your Windows screensaver, edit HOPSVR.PIF using the PIF editor and enter DEMO.HOP as program parameter. CAUTION: HOP's screensaver can detect mouse movements only if a mouse driver was loaded under DOS ! Optional Password Feature ───────────────────────── To prevent unauthorized access to your data while you leave the room, a security password can be set for the screensaver. When a password is set, the screensaver can be left only if the correct password is entered (or the computer is rebooted). To set, delete, or modify the password, enter HOP PASSWORD on the DOS command line and follow the instructions. The password will be safely encrypted and stored in HOP.INI. The password feature is only available for the registered version. If you use the screensaver in a DOS session under multitasking environments (Windows or OS/2) it doesn't make much sense to set a password because HOPSVR can't keep you from switching to the Program Manager or Workplace Shell. 'HOP Runs' Flag ─────────────── If you have the screensaver loaded and want to run (the interactive) HOP, you don't want the screensaver to popup all the time. For this reason, HOP creates a 'flag' file called HOPRUNS.TMP while it runs. The screensaver pops up but exits immediately if it finds this file. If for any reason the flag file doesn't get deleted when HOP ends, the screensaver won't run unless you delete the file manually or restart HOP to do it. ===================== HOP - Fractals in Motion ================= Page 12 ┌────────────────────────────────────────────────────────────────────────┐ │ WHAT DOES "HOP" MEAN ANYWAY ? │ └────────────────────────────────────────────────────────────────────────┘ Barry Martin from Aston University (Birmingham/England) discovered a new fractal in the mid-80's. A. K. Dewdney presented Martin's first images and the algorithm in his 'Computer Recreations' column in Scientific American (Sept.1986). He called the new fractal HOPALONG, referring to the unique way it grows on the screen. Unlike the famous Mandelbrot fractals, here the pixels 'hop from one point to another'. The fractal doesn't grow line by line, but rather emerges from the whole of the screen. The character of the resulting images is quite different from what most people associate with 'fractals'. Many Hopalongs have some mysterious similarity to some biological forms such as diatoms, radiolarians, or other unicellular microorganisms. (I strongly recommend to take a look at Ernst Haeckel's famous 'Art Forms in Nature' drawings.) If you find that the complexity and symmetry of such things fascinates you, you will also like HOP's creations. Maybe they will even make you wonder what the real connection is between nature, fractals, mind, and beauty. Hopalong fractals lack the deep complexity of the M-Set - it isn't possible to infinitely zoom into the images without losing some of their complexity. On the other hand, the way they are created is far more interesting to watch in real-time than the (usually boring) line-by-line growth of Mandelbrot fractals which results in utterly amazing, but static images (unless your computer is extremely fast). Appendix C contains a short Pascal program which shows how the Hopalong algorithm works. ──────────────────────── HOP is based on HOPALONG algorithms, but it introduces a lot of new and unusual features: Martin's formula is accompanied by more than two dozen newly developed formulas, all similar in structure, but different in detail. The result is a wide variety of new fractals. Several new mathematical 'special effects' modify the shapes of the 'pure' fractals and introduce movement and 'Fractals in Motion'. A wide variety of graphic effects is available to manipulate the images. Some of these effects are standard (VGA color scrolling is done by most graphic programs), but many others are unique and were designed for HOP. ===================== HOP - Fractals in Motion ================= Page 13 ┌────────────────────────────────────────────────────────────────────────┐ │ THE BASIC CONCEPT │ └────────────────────────────────────────────────────────────────────────┘ HOP runs like an slideshow. While some of the images in the show are more or less static, others contain wild or gentle movements and animations, depending on dozens of interacting parameters all of which you can control. Each of the slides runs endlessly or for a predetermined number of pixels. The slides are either 'composed', stored in a file, and can be exactly reproduced, or they are designed on-the-fly (improvised) by HOP's random algorithms or by you, or both. When you run the demo, HOP plays back a parameter file containing a series of 'composed' images and animations. (If you like HOP and learn how to use it, you will very soon also come up with interesting 'compositions' which you can exchange with other HOP users or run with the screensaver.) If HOP doesn't playback a file, it runs in an 'improvising' mode. Each of the images will run for a certain number of pixels, then a new image will come up, and so on. You have full control over all parameters, but unless you want to explore a specific image, you don't have to enter any numbers - everything will happen by itself! (Actually I started writing HOP because I'm so lazy.) While some of the images might blow your mind, others might be boring. The program juggles many variables, producing images that are based on controlled randomness - unfortunately, the program can't watch the images and decide if they are beautiful or not. The algorithms are blind. (Maybe this will be different in a future version of HOP). It is as if you took a snapshot of a random area of the Mandelbrot set - the chance to get a boring image is quite high even if the M-set contains loads of incredible sights. You have control over the decisions the program makes to some extent though - this happens on the 'Tune' page of the user interface. Take the randomly generated images as suggestions. Throw them away, or modify a nice image until you really like it. Then store it in your 'favorites' collection, and please exchange it with others. ===================== HOP - Fractals in Motion ================= Page 14 When you play with HOP's suggestions and learn to master all the different parameters, you will find that there are a number of effects that are almost never used in HOP's improvisations. They have to be used like the special effects in a movie or in rock music: Overusing them won't do any good, but using them thoughtfully can add spice and interesting variations. Also, some of the effects slow down performance or could easily make a boring picture if applied by a blind random algorithm. Another thing you should be aware of is that when running in random mode, HOP will try to automatically center and size the fractals. The reason this is done is that without this automatic optimization (just taking the naked random numbers and formulas and generating the images as they come), many fractal images would be too small, or you would be shown less interesting details, or the screen would be mostly blank because the fractal would develop right outside of it. The positive effect of this optimizing is that most images will be more or less interesting. You can sit and watch HOP design a neverending series of fractals, like the shells you find whilst walking along an ocean beach. But this is only one way of looking at them! Anyone interested in shells would stop from time to time and pick one up to look at its microstructure which - as we have learned from fractal theory - is just as complex as the view from above. HOP cannot do this for you automatically. It doesn't know where interesting details are located. The incredible microstructure of HOP fractals has to be studied manually. Try zooming in to interesting details and playing with the many program features and parameters to manipulate your view. HOP will reward you with an infinite world of complexity and beauty. ===================== HOP - Fractals in Motion ================= Page 15 ┌────────────────────────────────────────────────────────────────────────┐ │ THE USER INTERFACE │ └────────────────────────────────────────────────────────────────────────┘ There are two ways to interact with HOP: The hotkeys that can be pressed while the fractal is growing. The menu-driven user interface (from which you can control all of HOP's many parameters) which runs in text mode. Text mode is the mode your screen is in while you read this text (if you read it from the screen). You can't see the fractal from the user interface; you can't use the user interface menus while you see the fractal, so you will have to switch to the interface and back to the graphics. Hotkeys are the way to change the values of certain parameters while in graphics mode, plus there are a number of hotkeys that do different things, like saving or reading an image. Some of HOP's parameters can be controlled using keys as well as from the user interface pages. Think of HOP as a fractal synthesizer with the hotkeys being all the parameter controls (filters, oscillators etc). You must invest a little time to learn all those functions, but then you will be able to play like a virtuoso and do amazing things - faster and with more feeling than someone who accesses the menus everytime a parameter must be changed. To learn how pressing the hotkeys affects the fractal values, press the 'v' hotkey. Most of HOP's parameters will be displayed on the left side of the screen (to really see all values, you have to use a resolution above 640*400), and they change as you press a hotkey. ──────────────────────── Press the Enter key from the graphics screen to switch to the menus of the text mode user interface. The current image will be saved (you can switch off the save feature from the Configuration page of the user interface). Depending on your video hardware, you may or may not see a message 'Loading User Interface'. If the message is displayed for more than a fraction of a second, it is your video hardware that takes that long to switch. On a standard Tseng ET4000, the switching takes no time at all! ──────────────────────── The user interface consists of 8 pages that contain 8 different parameter 'departments': ┌────────────────────┬────────────────────────┐ │ Parameters that │ 1 - Fractal Values │ │ affect the current │ 2 - Math Effects │ │ fractal │ 3 - Graphic Effects │ │ │ 4 - Colors │ ├────────────────────┼────────────────────────┤ │ HOP Configuration │ 5 - Tuning HOP │ │ │ 6 - Configuration │ ├────────────────────┼────────────────────────┤ │ File Input/Output │ 7 - Read File │ │ │ 8 - Save File │ └────────────────────┴────────────────────────┘ ===================== HOP - Fractals in Motion ================= Page 16 On the first 4 pages you edit the parameters for the current fractal. Coming back from the user interface to the graphics screen, the fractal will either be restored and continued including the changes you applied, or it will be redrawn from the beginning (e.g. if you changed the formula). A little mark (*) in the upper right corner of the user interface pages indicates if the image has to be redrawn. Control keys on the text pages ╒═════════════╤══════════════════════════╤═══════════════════════════════╕ │ Key │ In a popup menu │ Not in a popup menu │ ╞═════════════╪══════════════════════════╪═══════════════════════════════╡ │ PgUp/Dn │ Move up/down │ Go to previous/next page │ ├─────────────┼──────────────────────────┼───────────────────────────────┤ │ Tab/ShiftTab│ - │ Highlight next/previous button│ ├─────────────┼──────────────────────────┼───────────────────────────────┤ │ Enter │ Choose a menu item │ Return to graphics, │ │ │ │ switch on the help screen, │ │ │ │ go to the highlighted page, │ │ │ │ or Quit (depending on which │ │ │ │ button is highlighted) │ ├─────────────┼──────────────────────────┼───────────────────────────────┤ │ Up/down │ Move up/down │ Move between data entry fields│ ├─────────────┼──────────────────────────┼───────────────────────────────┤ │ Space Bar │ - │ Pop up a menu in a field │ │ (or any │ │ (if this field has a menu) │ │ other key) │ │ or toggle On/Off │ ├─────────────┼──────────────────────────┼───────────────────────────────┤ │ Del, Esc │ Close an opened menu │ - │ ├─────────────┼──────────────────────────┴───────────────────────────────┤ │ F1 │ Switch context sensitive help on/off │ ├─────────────┼──────────────────────────┬───────────────────────────────┤ │ Mouse keys │ - │ Increment/decrement a │ │ │ │ numeric value while being │ │ │ │ pressed │ └─────────────┴──────────────────────────┴───────────────────────────────┘ There is context sensitive help for each of the data fields. Click on the Help button (or press Tab to highlight the Help button, then press Enter) to activate the help page. The help text will be displayed as you press Up/Down to move between the fields, or simply as you move the mouse across the fields. ──────────────────────── The following pages will explain most of HOP's features along with their corresponding entry fields on the 8 user interface pages. For those features that can also be controlled directly on the graphics screen using hotkeys, the hotkeys will also be mentioned. ===================== HOP - Fractals in Motion ================= Page 17 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 1: FRACTAL VALUES │ └────────────────────────────────────────────────────────────────────────┘ On this page you can choose a fractal formula and change the constants that are part of the formula. The formula and its constants are the mathematical basis for the image you will get. You can also change the maximum number of pixels for the image and the size and position of the fractal. ──Pixels Curr─────────────────────────────────────────────────────────── contains the number of pixels that have already been drawn for the current fractal. This value cannot be changed. ──Max─────────────────────────────────────────────────────────────────── contains the maximum number of pixels, or the 'lifetime' of the current fractal. Minimum value is 0, maximum value is 99999999 pixels. A value of 0 indicates that the fractal should run without a limit, i.e. until it is stopped manually. 'Max' is set to 0 by pressing the Ins key, or by changing any of the parameters that affect the image (HOP assumes that if you change colors, effects etc., you want to experiment with the current fractal, so it sets the lifetime to 0, letting you decide when to end the fractal). When running in improvising mode, HOP sets the maximum number of pixels for each new fractal to a random value. This value is related to the value of 'φ No. of Pixels' which can be set on the TUNE page. HOTKEYS= ins = 'keep' this fractal (Max = set to 0) ──Formula─────────────────────────────────────────────────────────────── HOP generates fractal images based on about two dozen internal formulas. All of the formulas are based on the structure of Barry Martin's original Hopalong formula (which is included as formula 'Classic'), but most of them were invented for HOP and have never before appeared anywhere else. The names of the formulas ('Classic', 'Lozenge' etc.) are loosely based on the corresponding fractal shapes (the fractals can look completely different with different fractal values or special effects). Especially in combination with the Transform effect (see below), there is a small chance that the values of a fractal diverge into positive or negative infinity, in which case HOP cannot continue with it. (Formulas 'Hexapod' and 'Threeply' are more likely to be unstable than others.) If this happens, there will be a message 'This fractal is not stable and cannot be continued'. If no key is pressed for 10 seconds, the fractal will end and a new one will be begun. If a key is pressed, it will be handled as a normal hotkey (i.e. [home] will repeat the unstable fractal, space bar will begin a new one, alt-t will try another Transform Constant, etc.). ===================== HOP - Fractals in Motion ================= Page 18 If you choose '(Pattern)' as formula, HOP won't draw any fractals. You can instead go to page 3 (Graphic Effects) and either choose a GIF image to load, and/or put together a wallpaper-like color pattern from the menus. You can even have fractals with background patterns - just choose one of the fractal formulas, then go to page 3 (Graphic Effects) and choose a GIF image or a black/white pattern and/or a color pattern. HOTKEYS= f/F = next/previous formula You cannot set formula 'Plankton' this way because this formula needs b values between -1 and +0.5 for interesting results. ──a,b,c,d─────────────────────────────────────────────────────────────── are the constants that are part of the fractal formula. (Most formulas only contain a subset of these four constants. The unused constants for each formula are blank and cannot be entered.) The constants a, b, and c can contain values from -999 to +999; however, the most interesting results lie between -50 and +50. A value of 0 is not allowed. The d constant can contain a value between 1 and 100. The 'plankton' formula requires the b constant to lie between -1 and +0.5. Press the '*' key from the graphics screen to set the constants to random values. This feature can be used to quickly get an idea of the multitude of forms produced by the current formula while keeping all other parameters (effects, etc.) unchanged. (If the Transform effect is switched on, different values for the constants won't change the image very much. Press ctrl-t to switch Transform off. See 'Math Effects' for information about Transform.) Press the '#' key from the graphics screen to resize/recenter an image (sometimes '#' has to be pressed several times to get the best result) after you have pressed '*', because with new random constants for the formula, the image can be too small or big or off the screen center. HOTKEYS= * = random values for a,b,c,d ──Horizontal/Vertical Position────────────────────────────────────────── Horizontal/vertical offset of the fractal. This is measured in pixels at 640*480 resolution (offsets at higher or lower resolutions are scaled appropriately), with 0 being the unmodified position of the very first pixel. Press the up/down/left/right cursor keys on the graphics screen to adjust the fractal position. Press ctrl-up/down/left/right for larger steps. If ctrl-up and ctrl-down don't work on your keyboard, try shift-up and shift-down instead. ===================== HOP - Fractals in Motion ================= Page 19 The position of the fractal will be symbolized by a rectangle that can be moved across the screen. Move the rectangle to the desired position, then press Enter to redraw the image. If the fractal is outside the screen borders, the borders will also be symbolized by a rectangle in the middle of the screen. This feature is helpful if you have lost track of the position of the fractal. If the screen is black and the action takes place outside of it, just press a cursor key and move the fractal rectangle back into the screen rectangle. HOTKEYS= left/right cursor keys = adjust position in small steps shift-left/-right === adjust in larger steps up/down cursor keys === adjust position in small steps shift-up/-down === adjust in larger steps # === correct size/position (try several times) ──Zoom────────────────────────────────────────────────────────────────── Zoom into the image by pressing the '+' or 'ctrl +' keys. Zoom out by pressing '-' or 'ctrl -' from the graphics screen. (Unlike Mandelbrot fractals, Hopalongs don't have an infinite depth; with a 10:1 zoom-in, nothing much will be happening on your screen.) Zooming will take place on a blank screen on which the fractal in its current state is represented by a rectangle. If the fractal becomes bigger than the screen itself, the screen will be represented by another rectangle. Press Enter to redraw the image. HOTKEYS= +/- === zoom in/out ctrl+/ctrl- = zoom in/out in big steps # === correct size/position (try several times) ===================== HOP - Fractals in Motion ================= Page 20 ──Erase Oldest Pixels─────────────────────────────────────────────────── If this setting is ON and the corresponding 'erase after' value is > 0, pixels will be erased as they "age". After the specified number of pixels has been displayed, the "oldest" ones will be erased. Maximum value is 32,000, but actually it depends on the amount of available memory. HOTKEYS= w toggle 'Erase Oldest Pixels' ctrl-f5 set erase queue length to 1 ctrl-f6 set erase queue length to maximum length f5 decrement by 1 f6 increment by 1 shift-f5 decrement in bigger steps shift-f6 increment in bigger steps All of these will also affect 'Pixels per Frame' and 'Color Frequency'. ──Show Every Nth Pixel────────────────────────────────────────────────── Usually, every computed pixel will be displayed. However, the structure and growth of symmetric fractals can be studied better if, for instance, only 1 out of 4 pixels is displayed (this can be accomplished by setting this variable to 4). If you manage to find a fractal with a triangular structure, try setting this value to 3. Interesting effects can be achieved in combination with Pixel Connect Type set to 'Colored Lines'. A setting of 1 (default value) will show all pixels. HOTKEYS= n = increment, N = decrement, ctrl-n = reset to 1 ===================== HOP - Fractals in Motion ================= Page 21 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 2: MATH EFFECTS │ └────────────────────────────────────────────────────────────────────────┘ On this page you can control four different HOP parameters that (for the sake of simplicity) are called 'mathematical effects'. This page is accessible only if a fractal formula was chosen. ──Rotate Image────────────────────────────────────────────────────────── If ON, the image will be rotated in three dimensions according to the x, y, and z angles specified in the next fields. If OFF, the x, y, and z angle settings are ignored. On the graphics screen, you can toggle Rotate with ctrl-r. To change the rotation angles of the fractal, press ctrl-pgup. This loads a rotation screen on which the current rotation angles are represented as a rotated rectangle on a blank screen with the rectangle sides drawn in different colors. Press Ins, Del, Home, End, PgUp, and PgDn to change rotation angles, Enter to redraw the fractal. In the current version, the center of the screen is not automatically the rotation center, but the fractal is rotated around its starting position. Rotating a fractal can therefore result in a changed position which must then be modified by pressing the cursor keys. HOTKEYS= ctrl-r = toggle Rotate ctrl-pgup = change rotation angles ──x,y,z───────────────────────────────────────────────────────────────── If Rotate Image is ON, these values are used to rotate the image in three dimensions. Angle is measured in radians. HOTKEYS= ctrl-pgup = change rotation angles ──Transform Fractal───────────────────────────────────────────────────── "Transform" is one of the "special effects" designed for HOP. After the Hopalong calculation, every pixel is recalculated based on another simple formula which includes a real number constant (the Transform Factor). If you toggle Transform (on the graphics screen) by pressing ctrl-T, you will notice that this is more than a special effect: it will change the image completely, producing an entirely new kind of fractal. HOTKEYS= ctrl-t = toggle Transform ===================== HOP - Fractals in Motion ================= Page 22 ──Transform Factor────────────────────────────────────────────────────── A real number constant which is part of the Transform formula. Changing this value will change the shape of the fractal. In fact, for each given Hopalong fractal with a certain formula and a value for a, b, and c, all the possible values for the Transform Factor produce a whole range of new fractal shapes. Similar values for the Transform Factor will produce similar shapes, and slowly incrementing the Factor will after a while reveal that the new shapes are forming a repeating series; one could say that they are 2-dimensional 'slices' of a 3-dimensional object. The 'Transform Animation' feature shows an animated succession of these 'slices'. HOTKEYS= t/T = increment/decrement the Transform factor alt-t = set Transform factor to a random value ──Transform Animation─────────────────────────────────────────────────── This unique kind of fractal animation draws consecutive "frames". In each frame, a transformed fractal is drawn with one value for the Transform Factor. For the next frame, the Transform Factor is incremented or decremented by a certain value. Then, while the next frame is drawn, the previous frame is being erased, but pixel by pixel - after drawing frame 200, pixel 10 comes erasing frame 199, pixel 10. The result is a series of fractals moving smoothly and changing shapes. (The "Erase Oldest Pixels" setting must be ON for best results.) The Animations can come in different types (consisting of typical settings for math effect and graph effect parameters) which are preset and roughly hard-wired in the program although all parameters are controllable. (You can decide how often you want to see each of the different 'Animation Type' presets ('Dancing Beads', 'Kaleidoscope', etc) by changing their percentages on the Tune page.) HOTKEYS= a = toggle Animation ──# Pixels per Frame──────────────────────────────────────────────────── If Pixels per Frame is set to a low value, the Transform Animation moves quickly, producing single pixels that jump or dance. If it is set to a very high value, the animation moves so slowly that it takes minutes to recognize it as an animation. HOTKEYS= ctrl-f5 set #pixels per frame to 1 ctrl-f6 set #pixels per frame to maximum length f5 decrement by 1 f6 increment by 1 shift-f5 decrement in bigger steps shift-f6 increment in bigger steps If you use those hotkeys, # Pixels per Frame will be synchronized with the length of the Erase Queue and the Color Frequency. ──Animation Speed─────────────────────────────────────────────────────── This controls the increment or decrement size for the Transform Factor while in Transform Animation mode. This will determine the step rate and speed of the animation. ===================== HOP - Fractals in Motion ================= Page 23 ──Animation Forward───────────────────────────────────────────────────── In Transform Animation mode, this setting determines if the Transform Factor will be incremented or decremented. HOTKEYS= < / > toggle decrement / increment Transform Factor ──Rotate Animation────────────────────────────────────────────────────── Determines if the animated fractal should also be rolling around its x, y, and/or z axis while it crawls across the screen. HOTKEYS= alt-a = toggle Animation Rotate ──Rotation Speed──────────────────────────────────────────────────────── Determines the speed of the rotation while in Transform Animation mode. ──Warp Type───────────────────────────────────────────────────────────── The two kinds of "Warp" are HOP specific mathematical "special effects". Both are independent of the Transform and Animation features. Spirals: the fractal will 'explode' from the inside, developing spirals and tube extensions which can add quite dramatic effects. Eyes: the fractal will develop concentric rings and ellipses. Looks best without colorscroll and with very detailed palettes. The 'eyes' warp type uses a color mapping method that differs slightly from HOP's usual Linear color mapping: Color assignment is linked to Warp Frequency. HOTKEYS= k = toggle Warp = Spirals/Eyes K = Warp off ──Warp Frequency──────────────────────────────────────────────────────── With Warp = 'Spirals', Frequency determines the speed of the spiral growth and the resulting movements. With Warp = 'Eyes', it determines how often the fractal will jump into systems of concentric ellipses. HOTKEYS= ctrl-k = set a random value for warp frequency ──Warp Depth──────────────────────────────────────────────────────────── With Warp = 'Spirals', Depth determines the maximum length of the spirals With Warp = 'Eyes', it determines how strongly the fractal will be 'distorted' or altered by systems of concentric ellipses HOTKEYS= alt-k = set a random value for warp depth ===================== HOP - Fractals in Motion ================= Page 24 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 3: GRAPHIC EFFECTS │ └────────────────────────────────────────────────────────────────────────┘ This page allows you to control a number of parameters that affect the graphical representation of HOP's mathematical results. This is the page for artists! Mathematical purists won't be interested in this stuff. ──GIF Image───────────────────────────────────────────────────────────── A background chosen from this GIF Image menu will use any GIF image as background for a HOP fractal (this can be used to develop multi-fractal images). A GIF image can also be modified by a Plasma color pattern (see below). To load GIF images from the menu, they must be located in the GIF image directory that you specified on the Configuration page (see below). When you load a GIF image as background for a fractal, HOP's current videomode will automatically be set to the videomode that shows the image full-screen. The videomode will be permanently changed: If you run HOP with 1024*768 pixels resolution and load a GIF image with 320*200 pixels, the subsequent resolutions will be 320*200 until you manually change the resolution. The current palette will be overwritten by the palette contained in the image file. One of the 'expert level' features of HOP is its ability to generate multiple images. Save a HOP image to a GIF file (see Save page) and load the resulting image file as the background for a new fractal - there you have a multiple image ! Save the resulting image to another GIF file and repeat the process - and so on. All of this can even be automated (see Save page)! ──Black/White Pattern─────────────────────────────────────────────────── A background chosen from the 'Black&White Pattern' submenu will draw one of 12 regular black+white stripes patterns, a starfield 'deep space' pattern, or concentric ellipses. The black/white patterns can be used as background patterns either for fractals or for a Plasma cloud. (Try b/w ellipses in combination with Plasma.) HOTKEYS= d/D === set next/previous black/white pattern ctrl-d = no pattern ===================== HOP - Fractals in Motion ================= Page 25 ──Color Pattern───────────────────────────────────────────────────────── A background chosen from the 'Color Pattern' submenu will display various colored background patterns. In the current version, HOP can draw 7 different background patterns (Plasma, Connett Circles, Rings, Squares, Horizontal, Vertical, and Wheel) some of which are already very complex in themselves and can be run alone, whereas others are just simple stripes that become complex when overlaid with other patterns. You can overlay several patterns by choosing more than one from the menu. Consecutively drawn patterns will be overlaid either in 'XOr' or in 'Or' mode. (The color number of each new pixel gets xor-ed or or-ed with the color number of the previous pixel). 'XOr' overlays look like complex systems of shrinking/growing rectangles. 'Or' overlays feature simple fractals of the Sierpinski triangle type. In their purest form, these two overlay methods can be watched by overlaying the 'Horizontal' and 'Vertical' stripe patterns. After this, watch wandering groups of warped and squeezed Sierpinski triangles wander across the screen by simply overlaying 'Rings' and 'Horizontal' in 'Or' mode ! In the color pattern submenu, switch 'XOr' and 'Or' mode for each pattern by pressing the space bar, then press Enter. The resulting combination of patterns is displayed in a window containing the first letters of the pattern names (p c r s h v w) with an 'x' for XOr mode or an 'o' for Or mode underneath. The 7 different basic color patterns are: 1. Plasma The Plasma clouds algorithm is based on a Pascal program source by Bret Mulvey distributed as PLASMA.ARC. Tim Wegner (one of the FRACTINT authors) modified the algorithm for Fractint. HOP uses a modified version of his version. For a better performance, HOP Plasma clouds can be symmetric. Fractint describes plasma clouds like this: "Random, cloud-like formations. Requires 4 or more colors. A recursive algorithm repeatedly subdivides the screen and colors pixels according to an average of surrounding pixels and a random color, less random as the grid size decreases." When experimenting with plasma clouds, hitting F10 (=set a new random seed and redraw) will redraw the plasma pattern with different shapes. The granularity of the Plasma clouds can be set on the 'Graphic Effects' page. A low value produces very smooth color surfaces. A high value for granularity will look very chaotic. ===================== HOP - Fractals in Motion ================= Page 26 Plasma clouds will react to what is already on the screen. Combinations with black/white patterns are very nice, but Plasma can also overlaid over a GIF image (just choose a GIF image name from the GIF image menu) - this works best with images that are very minimalistic. Additionally, Plasma clouds can be overlaid over a finished Hopalong fractal. See "Plasma Overlay" on the Colors page. 2. Connett Circles were invented by John E. Connett (University of Minnesota). He found that interesting moire effects can be produced by simply associating the result of x*x + y*y (computed for each screen position) to colors. His findings were presented in A.K.Dewdney's Scientific American article along with Hopalong fractals. Connett Circles can be viewed with different values for 'Connett Circle Zoom' which can be set on the 'Graphic Effects' page. This zoom is actually inversed: A low value produces close-ups of the circles with very smooth colors. High values will result in a matrix of circle moirés. 3. Rings 'Rings' are nothing but concentric circles drawn with consecutive colors. 4. Squares, 5. Horizontal, 6. Vertical These are simple but beautiful stripe patterns. Try different video resolutions. 7. Wheel Consists of radial lines. If 'randomseed' (which can be changed by pressing hotkey F10) is an odd number, the wheel will cover the whole screen, else the lower half only (resembling an airport runway). Switch pattern 1 - 7 to xor / or / off by pressing Alt-1 to Alt-7 from the graphics screen. (Pressing a shift key at the same time will work the other way around.) HOTKEYS= alt-0 = drop formula and draw just a color pattern (shift)alt-1 to (shift)alt-7 = color patterns ──Plasma Granularity──────────────────────────────────────────────────── If Plasma clouds are contained in the current pattern combination, this value determines the granularity of the clouds. A low value makes very smooth clouds, a high value will produce very grainy clouds. Values can range from 0 to 10000. ===================== HOP - Fractals in Motion ================= Page 27 ──Connett Circle Zoom─────────────────────────────────────────────────── If Connett circles are contained in the current pattern combination, this value can be used to control their magnification. A low value will produce bigger circles. Try values between 100 and 500. The circles will look very different with different color maps. Maps with very smooth color shadings will produce the clearest circles. Values can range from 0 to 32767. ──Pixel Shape─────────────────────────────────────────────────────────── Usually, the word 'pixel' stands for a dot on a computer screen. That meaning has been a little expanded here. In HOP, pixels can have different shapes. Changing the pixel shape will change the appearance of a fractal in a dramatic way. In addition, almost all pixel shapes are scalable ! Possible pixel shapes in this version are: - None : means that no pixels will be drawn. (It may happen that you run HOP and the screen will stay blank. The reason could be that you accidentally switched Pixel Shape to None.) This setting can be useful in combination with the Grid effect, or with Lines. If you experiment with a Background Image (Connett Circle, Plasma, or GIF), you can switch off HOP's fractal drawing on purpose by setting Pixel Shape to None. - Pixel/Circle: The classic dots as they are supposed to be (until you start blowing them up changing their Pixel Size, in which case they will turn to circles). You can also set 'Elliptic' to ON which will turn the circles into ellipses that change shape with size and position. Depending on the settings of 'Elliptic', 'Pixel Fill', and 'Reflection', you will get 3-D like beads or soapbubbles. - Rectangles: Depending on the value of 'Elliptic', HOP will either draw squares or rectangles (that change shape with size and position). - Fourangles: are parallelogram shaped pixels that change shape with size and position in a way that depends on the position of the previous pixel. Try with concentric fill style. - Tryangles : are triangular pixels that change shape with size and position in a tumbling kind of way that can be watched best in a 'Dancing beads' type animation. - Triangles : are triangular pixels that change shape with size and position in a way that depends on the position of the previous pixel. - Lines : a short line is drawn from the current pixel pointing towards the position of the previous pixel. This pixel shape will display some of the otherwise invisible dynamics of fractal growth. - Flakes : Spiky pixels that change shape with size and position. ===================== HOP - Fractals in Motion ================= Page 28 - Fuzzy : Fuzzy clusters of pixels that look as if they were sprayed. At a closer look, they resemble crawling bugs. - Brush : This pixel shape is similar to movements of a broad brush, or to soft chewing gum being pulled into strings. For each pixel drawn, the Brush algorithm searches its neighborhood for pixels of the same color and draws a line towards them. The intensity of the Brush shape effect depends on Pixel Size and on Color Frequency - the slower the colors move, the 'stickier' the chewing gum. Brush pixels tend to be slow! - Colorsquares : squareshaped pixels of a fixed size. Each of the squares is a miniature copy of the palette editor 16 * 16 color matrix (see Palette Editor chapter) and contains all 256 VGA colors that are currently set. This feature allows you to create 'sprites' (tiny images that move across the screen) simply by designing an appropriate color map using HOP's palette editor which contains a 'drawing' feature. Sprite images don't have to be square shaped. Just switch off the unused parts of the square by assigning them an RGB value of (0,0,0) which is ordinary black. Those parts of the sprite that are *supposed* to be black can then be drawn with an RGB value of (0,0,1), which is almost black. - Comment : This pixel type displays a text string instead of a dot. If the current fractal has already been assigned a comment (enter a comment on the 'Save' page), the comment will displayed, otherwise the text string will contain random characters. Text strings are written horizontally or vertically depending on the value of 'Elliptic'. HOTKEYS= x / X = next / previous pixelshape alt-x = 'pixel' shape ctrl-x = no pixels ──Elliptic────────────────────────────────────────────────────────────── With 'Elliptic' set to ON, - pixels of the 'Pixel/Circle' shape will appear elliptic instead of circular - pixels of the 'Rectangle' shape will appear as rectangles instead of squares - 'Lines' and 'Fourangle' pixels will point into a different direction - 'Comment' pixels will write vertical text strings. HOTKEYS= q === toggle Elliptic Pixels ===================== HOP - Fractals in Motion ================= Page 29 ──Pixel Size──────────────────────────────────────────────────────────── This setting will determine the size of the pixels. Generally, the bigger they are, the slower HOP will run. HOTKEYS= i === increase pixel size I === decrease pixel size alt-i = reset pixel size to 1 and switch Oscillate off ──Pixel Oscillate─────────────────────────────────────────────────────── If set to ON, pixel sizes will oscillate between 1 and the size set in 'Pixel Size'. This can produce weird 3-D effects. (If Pixel Size is set to 1, the oscillations will be determined randomly.) The speed of the size oscillation is determined by the color frequency! With colors fastly changing, the oscillation will also be fast. HOTKEYS= ctrl-i = toggle Pixel Oscillate ──Pixel Fill──────────────────────────────────────────────────────────── Pixels of the types Pixel/Circle, Rectangles, Triangles and above a certain size will be filled with one of 13 fill patterns. The 'Connett' pattern is only available for Pixel/Circle. The 'Concentric' pattern is only available for Pixel/Circle and Rectangles. HOTKEYS= z / Z = next / previous fill pattern ctrl-z = 'solid' fill ──Reflection──────────────────────────────────────────────────────────── With Reflection set to ON, circular/elliptic pixels will display a white reflection-like spot which will give them a striking 3-D look. Other pixel types will also display white spots in various ways. HOTKEYS= ctrl-q = toggle Reflection ──Border──────────────────────────────────────────────────────────────── Big pixels (circles, rectangles, triangles) will have their shape outlined in black with Border set to ON. HOTKEYS= alt-q = toggle Border ──Symmetry────────────────────────────────────────────────────────────── Symmetry can either be None, Vertical, Horizontal, Cross, or Diagonal. Vertical means that each pixel is duplicated across the vertical axis; ie, for every pixel (x,y), a pixel is also drawn at (-x,y). Horizontal means that each pixel is duplicated across the horizontal axis. Cross is both. Diagonal duplicates each pixel diagonally. HOTKEYS= y / Y = next / previous symmetry type ctrl-y = no symmetry ===================== HOP - Fractals in Motion ================= Page 30 ──Pixel Connect Type──────────────────────────────────────────────────── Consecutive pixels can be connected by lines. Options (and their corresponding hotkeys) are: Background (alt-l): lines of background color are invisible but they make the pixels that they cross "disappear". This looks like parts of the image are fading away. Colored Lines (l): produce lattices, and sometimes a surface effect, as in "Kaleidoscope" type animations. Conditional (L): colored lines that are drawn on background color only, thus not obscuring colored pixels. Slow! NoErase (ctrl-l): Same as Colored Lines, but the lines won't be deleted even if Erase Oldest Pixels is ON. There is only one situation in which using this line type will have an interesting result: If Erase Oldest Pixels is ON and Tie Colors (see below) is ON, like in Dancing Beads type animations. If you have Dancing Beads jumping across the screen, press ctrl-l. The resulting lines will have tied colors. This looks somewhat different from Kaleidoscope type lines. HOTKEYS= alt-l = toggle 'Background' type lines l === toggle 'Colored Lines' type lines L === toggle 'Conditional' type lines ctrl-l = toggle 'NoErase' type lines ──Line Style──────────────────────────────────────────────────────────── This determines the look of a line. A line style of 0 (default) is a solid line. Any other number will produce dotted lines with the dot pattern being a representation of the 'Line Style' number in a 16-bit format. (Try 43690 for a 1010101010101010 pattern. If you want to design your own line styles, take a calculator program like Sidekick, enter 16-digit binary numbers that look like the pattern you want, and enter their decimal values into Hop.) HOTKEYS= j = toggle Line Style = solid/dotted ──Thick Lines─────────────────────────────────────────────────────────── Lines can be thin or thick. This will affect some of the pixel shapes as well as the connecting lines and grids. Thick lines are slower than thin lines. Careful: using thick lines will also slow other things down. Most of the pixel types will be drawn considerably slower with thick lines especially if pixel size is higher than 2. HOTKEYS= / = toggle line thickness ===================== HOP - Fractals in Motion ================= Page 31 ──Shadow──────────────────────────────────────────────────────────────── HOP can add a shadow to the fractal, or to each pixel. This is nothing but a simple graphic effect, but it changes the character of the image in a dramatic way, giving it depth and substance. Two shadow types are possible: - Background Only: a shadow pixel will be drawn only if its position isn't occupied by a fractal pixel. This will produce a shadow underneath the fractal body, making it hover above the ground unless black is the background color. If the background is black, this shadow type is useless because you cannot see it, but it will slow down performance a little anyway. If you use a color pattern or GIF background, this shadow type won't work because there is no screen position left blank. - Always : a black shadow pixel will be drawn even if this will obscure a fractal pixel. This will produce a strong 3-D effect, especially with pixel types that are bigger than a simple pixel (e.g. 'Bubble' pixels). This shadow will also be visible with a black background, as well as on color pattern or GIF image backgrounds. HOTKEYS= o = change shadow type O = no shadow ──Shadow x, y distance────────────────────────────────────────────────── The Shadow X Distance and Shadow Y Distance values (measured in pixels) are used to determine the shadow placement. ──Twinkle Frequency───────────────────────────────────────────────────── Determines how often pixels will "twinkle". This effect looks nice (especially on a dark background), but slows down performance considerably. If you have a slow computer, lowering this value will increase fractal growth speed. (You can set the "Slow Pixels" setting to a low value in the "Tune HOP" screen to limit how often this effect will be used.) HOTKEYS= . = toggle Twinkle effect ──Grid────────────────────────────────────────────────────────────────── The Grid effect - one of the rather experimental features of HOP - draws lines in addition to a pixel. Each line will extend from the pixel position across the screen until it meets another line. Grids can come in various types: - Barcodes go straight downward which gives the image a barcode look; - Squares and - Hexagon add a certain Bauhausian touch; - Random this type resembles broken glass. HOTKEYS= g / G = next / previous grid type ctrl-g = no grid ===================== HOP - Fractals in Motion ================= Page 32 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 4: COLORS │ └────────────────────────────────────────────────────────────────────────┘ HOP's colors are based on the VGA 256 color system. HOP can also be run under a 16 color EGA system (it will display the first 16 colors out of the current VGA spectrum) but of course with considerably less appeal. In VGA and related color video systems, each pixel that is displayed on the screen is assigned not only a position but also a color number. Color numbers reach from 0 to 255. Each of the color numbers has a red, green, and blue component with intensity values reaching from 0 to 63. This is enough to create a multitude of colors. A set of 256 colors (0-255) is usually called a palette map. HOP palette maps can be read from and stored in ascii files; these files have the extension .MAP and are compatible with Fractint's map files (see appendix for information on Fractint). Fractint's 'home' is in the Compuserve GRAPHDEV forum. Compuserve users can download hundreds of incredible color map files from here. For those without Compuserve access, HOP contains three different palette map generation algorithms, but most of the map files in the Compuserve forum are hand-designed and therefore much more interesting than automatically generated or random color maps. However, with HOP's palette editor you can design your own palette maps and save them as Fractint compatible .MAP files. Of HOP's 256 colors, only 253 are used to draw the fractal itself. - Color #0 is always the background color; - Color #1 is always white (its RBG values are set to 63,63,63) unless you change it manually using the palette editor. The white color of #1 must be white for various special effects (e.g. the light reflection on the Bubbles pixels) and for the values display. - Color #2 is always black (unless you change it manually) and is used to draw shadows. One of the amazing things you can do with VGA colors is a special effect called 'colorscroll'. The colors are scrolled simply by moving the RGB values of each of the color numbers to the previous number (with color 255 being set to what used to be color 0), adding another dimension of movement to HOP. ===================== HOP - Fractals in Motion ================= Page 33 ──Frequency───────────────────────────────────────────────────────────── Usually, the colors in HOP are assigned to the pixel in a sequential order. 'Color Frequency' represents the number of pixels of the same color that will be drawn before shifting to the next color in the palette. The lower the frequency, the faster the color will change. With a high frequency value, large parts of the image will be drawn with the same color. If color frequency is too high, colorscroll will begin to stutter; if it is too low, the colorscroll speed will give you a headache. On the graphics screen, press number keys between 0 and 9 to control the color frequency (0 means that colors will change for each pixel; 9 means color changes every 1000 pixels) or shift-up/down. Color frequency also determines oscillation speed. HOTKEYS= 0,1,2,..,9 === set color frequency to 1,..,1000 shift-up/shift-down = inc/decrement color frequency ──Palette Mode────────────────────────────────────────────────────────── HOP has three ways of producing random palettes, plus an option to read color palette .MAP files. Periodic Periodic changes in hue with several overlaying frequencies. Irregular Random color palettes that contain contrast colors, soft shades, and occasional stripes. Continuous This palette mode is supposed to be used in combination with colorscroll. It produces a smooth (but somewhat granular) palette that doesn't repeat when scrolled, but rather keeps on changing. There are occasional complementary colors thrown in. Fractint Map reads colors from a .MAP file. If there are such files on your harddisk (in the directory specified on the Configuration page), you can choose from them in a popup menu. If no Fractint maps are found, HOP will use one of the other three color algorithms. HOTKEYS= P = set periodic palette p = set irregular palette alt-p = set continuous palette ctrl-p/P = load next/previous Fractint MAP E = edit the current palette ──MAP Filename────────────────────────────────────────────────────────── If a Fractint Map was chosen for Palette Mode, HOP loads a ready-made Fractint .MAP color file. These files must be located in the directory that you specified on the Configuration page. HOTKEYS= ctrl-p / P = load next / previous Fractint MAP ===================== HOP - Fractals in Motion ================= Page 34 ──Color Mapping───────────────────────────────────────────────────────── A 'linear' color mapping will assign colors to pixels in a sequential succession, as described above (n pixels will be drawn with color 27, then n pixels will be drawn with 28, and so on). If the 'Eyes' Warp effect is on, colors are also assigned in a sequential succession, but depending on the value of Warp Frequency. A 'vortex' color mapping will roughly look as if the fractal was overlaid by color rings or spirals coming out of the center. The colors are assigned depending on the pixel's distance to the previous pixel. A similar mapping method is 'radial'. 'Vortex' and 'radial' mappings look best with fractals that have an interesting shape but lack an interesting inner structure, like 'plankton' formula fractals. HOTKEYS= h / H = next / previous Color Mapping ──Colors tied─────────────────────────────────────────────────────────── This setting is necessary for a 'Dancing Beads' type animation. 'Tying' the colors to the pixels has the effect that each pixel will keep its color while moving along. (Actually it will only keep its color number - switch colorscroll on/off with tied colors in 'Show Values' mode to see what this means. Technically, the color numbers are assigned to each pixel's position in the Erase queue.) With Erase Oldest Pixels switched off, this setting will simply give each consecutive pixel a new color. HOTKEYS= C = toggle Colors Tied (use capital C !) ──Colorscroll─────────────────────────────────────────────────────────── You can switch colorscroll on and off and determine its direction. Colorscroll speed depends directly on the Color Frequency. In HOP, the colors are scrolled *while the fractal grows*. HOTKEYS= c === toggle Colorscroll alt-c = toggle Static Colorscroll (see below) shift-left/shift-right = scroll up/down for 1 color If you change the default values for 'from' and 'to', the scrolling region of colors will be limited. Some parts of the image will stand still while others will move as their colors scroll. ──Scroll Upward──────────────────────────────────────────────────────── Controls the "direction" of the colorscroll motion, referring to the direction of the color palette's movement on the 'Show Values' window. If 'Linear' color mapping is used, and colors are scrolling downward, set 'Colorscroll From' to 4 instead of 3 if you want to synchronize the new pixel color assignment with the scroll. This will set every new pixel to the same color. Yes I know this sounds difficult but it is actually very simple ! HOTKEYS= ctrl-c = toggle Colorscroll direction ===================== HOP - Fractals in Motion ================= Page 35 ──Pulsate─────────────────────────────────────────────────────────────── This effect makes the RGB values of each color bounce up and down. Red will turn to green and back to red, etc. Pulsation speed is determined by Color Frequency. It can be used independently of Colorscroll. HOTKEYS= u = toggle color pulsation ──Color Divide────────────────────────────────────────────────────────── If you use colored background patterns, the foreground fractal might be difficult to see because it shares its colors with the background. With Color Divide set to on, you can specify which subset of the color map (3 - n) will be used by the background and which (n+1 - 255) will be used by the foreground. Nice effects can be produced by combining this with a limited color scroll range. ──Static Colorscroll ─────────────────────────────────────────────────── With static colorscroll, fractal growth freezes while the colors are moving. This will make the colors scroll very smoothly - the program doesn't have to stop and think about the position of the next fractal pixel. A number > 0 entered on the 'Static Colorscroll' field will not turn on static colorscroll immediately. If you play a fractal from a parameter file, HOP will first develop the fractal as usual - it will draw n pixels with n=Maxpixels as specified on the 'Fractal Values' page. Then, if HOP finds that there is a value for 'Static Colorscroll', it will scroll the colors on the finished image. This will look great for very detailed colorful images. Colorscroll speed is determined by the 'Colorscroll Delay' configuration setting. HOTKEYS= alt-c = toggle static colorscroll During static colorscroll, you can use the hotkeys for color frequency, scroll direction, and palette modes. Every other key will switch off static colorscroll and then perform its function, if it is assigned a function. If you enter a value here, the fractal can't run forever: Maxpixels (specified on the 'Fractal Values' Page) must be > 0 ! ──Plasma Overlay ─────────────────────────────────────────────────────── A fractal image can be overlaid by a plasma pattern which will change the look of the image in a dramatic way. The plasma cloud will be generated after the fractal image is completed. After this, there will be a period of static colorscroll. Try Plasma Overlay with a sparsely drawn fractal on black/white patterns and grids, spiced with a palette mostly in grey colors ... This feature is only accessible if 'Static Colorscroll' has a value. ===================== HOP - Fractals in Motion ================= Page 36 ┌────────────────────────────────────────────────────────────────────────┐ │ HOP'S PALETTE EDITOR (registered version only) │ └────────────────────────────────────────────────────────────────────────┘ Press E from the graphics screen to enter HOP's palette editor. The current 256 colors will be displayed as a 16 * 16 matrix. You can edit single colors or groups of colors, scroll the palette, save the current palette to a MAP file, and load a new MAP file. Each of the 256 colors (counted from 0 to 255) consists of a red, green, and blue component each of which has an intensity value between 0 and 63. Color #0 is the background color; color #1 is always white, and #2 always black. Colors #1 and #2 can be manually edited, but then several things don't work quite as they should: If #1 is edited, light reflections on Bubble pixels and similar effects won't be white anymore, and the text on the 'Show Values' screen might be unreadable. If #2 is edited, shadows won't be black anymore. Use the cursor keys to select one of the colors. Then press one of the palette editor hotkeys ... after modifying the palette, press Enter to return to the fractal. One of the interesting features of this palette editor is called 'drawing'. Press a shift key and move around using the cursor keys to see what this means. 'Drawing' is nice if you want to play with the 'colorsquare' pixel type which turns the current palette into a sprite. ===================== HOP - Fractals in Motion ================= Page 37 ╒════════════════════════════════════════════════════════════════════════╕ │ PALETTE EDITOR HOTKEYS │ │ │ ├─GENERAL─────┬──────────────────────────────────────────────────────────┤ │ Enter │ returns to the graphics screen │ │ Esc │ exits to DOS │ │ │ │ ├─COLOR MODIFICATION─────────────────────────────────────────────────────┤ │ Ins/Del │ Inc/dec the red component with shift = inc/dec by 8 │ │ Home/End │ Inc/dec the green component with shift = inc/dec by 8 │ │ PgUp/PgDn │ Inc/dec the blue component with shift = inc/dec by 8 │ │ alt-R │ Swap red and green │ │ alt-G │ Swap green and blue │ │ alt-B │ Swap blue and red │ │ shift- │ │ │ cursor keys│ Draw lines │ │ │ │ ├─PALETTE SHIFTING/SCROLLING─────────────────────────────────────────────┤ │ < > │ Scroll left/right by 16 │ │ , . │ Scroll left/right by 1 │ │ C │ colorscroll │ │ ctrl-C │ change colorscroll direction │ │ │ │ ├─COLOR GROUP OPERATIONS─────────────────────────────────────────────────┤ │ A │ Anchor (mark color #1) │ │ O │ Copy color #1 to color #2 │ │ W │ Swap color #1 and color #2 │ │ = │ Graduated shading between color #1 and color #2 │ │ ~ │ Granular shading between color #1 and color #2 │ │ │ │ ├─READ / SAVE PALETTES───────────────────────────────────────────────────┤ │ P │ set a periodic palette │ │ p │ set an irregular palette │ │ alt-P │ set a continuous palette │ │ ctrl-p │ Read next map file │ │ ctrl-shift-P│ Read previous map file │ │ R │ Read specific MAP file │ │ S │ Save to MAP file │ │ ctrl-bkspace│ restore palette (undo all changes) │ └─────────────┴──────────────────────────────────────────────────────────┘ ===================== HOP - Fractals in Motion ================= Page 38 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 5: TUNING HOP (registered version only) │ └────────────────────────────────────────────────────────────────────────┘ When not playing back a parameter file, HOP improvises freely. Unless you have changed parameters (causing HOP to stay with the current fractal), there will be a constant succession of random images and random animations, with many of HOP's special effects switched on in random combinations. All of these random decisions are weighted and based on certain percentages most of which you can modify on the Tune page. The next time you run HOP, it will remember your settings. This is called 'Tuning HOP'. ──φ No. of Pixels──────────────────────────────────(Default:64000)────── The average number of pixels that will be generated for a fractal before it moves on to the next image. Set this to a high value if you prefer to look at images for a long time. Set it to a low value if you are impatient. 'Average' indeed means that HOP will vary the number of pixels for each fractal, based on random and the number entered here. It also tries to adjust the value for slower running fractals. ──Density──────────────────────────────────────────(Default:2)────────── Determines the complexity of animations (i.e. average frame length and erase queue). On slow PCs, animations involving many pixels won't run smoothly; on fast PCs, animations with few pixels run too fast. If you have a relatively slow 386 (or below), set Density to 1. Try a value of 5 or 10 for faster 486 systems, and even higher values for extremely fast PCs. HOP tries to estimate the best density for your machine after the initial video installation. ──Patterns Only%───────────────────────────────────(Default:2)────────── The percentage of color pattern combinations running instead of Hopalong fractals. ──Transform%───────────────────────────────────────(Default:25)───────── The percentage of fractals that will employ the Transform effect. Set this to a low value if you are a 'fractal purist' who wants to see unmodified Hopalong-type fractals. ──Animation%───────────────────────────────────────(Default:35)───────── The percentage of fractals that will employ Animation. If you have a slow machine (especially if you have no math coprocessor), you should set this setting to a low value because animation is very floating-point intensive and looks good only on fast machines. ──Warp Effects%────────────────────────────────────(Default:25)───────── The percentage of fractals that will employ Warp Effects. Set this to a low value if you are a 'fractal purist' who wants to see unmodified Hopalong-type fractals. ===================== HOP - Fractals in Motion ================= Page 39 ──Rotation%────────────────────────────────────────(Default:50)───────── The percentage of fractals that will employ Rotation. Set this to a low value if you are a 'fractal purist' who wants to see unmodified Hopalong-type fractals. ──Symmetry%────────────────────────────────────────(Default:10)───────── The percentage of fractals that will employ Symmetry. Set this to a low value if you are a 'fractal purist' who wants to see unmodified Hopalong-type fractals. Set it to a high value if you like pretty ornaments, mandalas etc. ──Slow Pixels%─────────────────────────────────────(Default:1)────────── Some Pixel Types (Brush, Triangles, etc) and some pixel settings (Twinkle effect, Big Pixels, etc) take considerable processing overhead. This value controls the percentage of fractals that will employ these "slow" pixel techniques. If you have a slow machine, you should set this setting to a low value. ──Shadow%──────────────────────────────────────────(Default:90)───────── The percentage of fractals with Shadows. ──Colorscroll%─────────────────────────────────────(Default:75)───────── The percentage of fractals that will employ Colorscroll. If you find that your screen flickers badly while scrolling the colors, you can set this setting to a low value or even to zero. (Then tomorrow morning go and buy a better video card and monitor, because you are missing some of HOP's best effects.) ──Black Background%────────────────────────────────(Default:50)───────── The percentage of fractals with a black background. If you want to have the blackness of space as background for your fractals all the time, set this to 100%. If you like shadows, set it to a low value and Shadows% to a high value. ──Slow Changes%────────────────────────────────────(Default:50)───────── The percentage of animated fractals that will use the Slow Changes animation type. Slow Changes is good for the lovers of minimalism (people who like to listen to Brian Eno's ambient music or La Monte Young / Marian Zazeela's music/light performances). In this mode, the Erase Queue is long and Animation Speed (increment or decrement size for the Transform Factor) is small. HOTKEYS= alt-f1 sets this animation type temporarily. ===================== HOP - Fractals in Motion ================= Page 40 ──Fast Changes%────────────────────────────────────(Default:10)───────── The percentage of animated fractals that will use the Fast Changes animation type. Fast Changes employs low values for # Pixels per Frame and high values for Animation Speed. Animations moves quickly. HOTKEYS= alt-f2 sets this animation type temporarily. ──Lines%───────────────────────────────────────────(Default:10)───────── The percentage of animated fractals that will use the Lines animation type. This mode looks like a mesh of wandering lines. HOTKEYS= alt-f3 sets this animation type temporarily. ──Dancing Beads%───────────────────────────────────(Default:10)───────── The percentage of animated fractals that will use the Dancing Beads animation type. The Dancing Beads (lyrical name, eh?) looks best with the 'Pixel/Circle' pixel shape, an Irregular palette, and Tied Colors. In this mode, # of Pixels per Frame must be the same as the Erase Queue length (synchronize these values by pressing F7). HOTKEYS= alt-f4 sets this animation type temporarily. ──Kaleidoscope%────────────────────────────────────(Default:20)───────── The percentage of animated fractals that will use the Kaleidoscope animation type. Most people seem to like this animation type best. Good for generating Rorschach tests. Kaleidoscope uses colored Pixel Connect types, i.e. lines that are drawn between subsequent pixels. HOTKEYS= alt-f5 sets this animation type temporarily. ──Periodic Palette%────────────────────────────────(Default:20)───────── The percentage of fractals that will use the Periodic palette mode. ──Irregular%───────────────────────────────────────(Default:30)───────── The percentage of fractals that will use the Irregular palette mode. ──Continuous%──────────────────────────────────────(Default:20)───────── The percentage of fractals that will use the Continuous palette mode. ──Fractint Map%────────────────────────────────────(Default:30)───────── The percentage of fractals that will get their colors from a Fractint color map. If you have many Fractint maps, set this to a high value because generally, they are more interesting than the color palettes generated by HOP. If you have only a couple of map files, don't set it to a high value because then you will see the same colors most of the time. ===================== HOP - Fractals in Motion ================= Page 41 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 6: CONFIGURATION │ └────────────────────────────────────────────────────────────────────────┘ HOP's configuration items are stored in a file called HOP.INI. ──VESA Compatible─────────────────────────────────────────────────────── shows if your video card is VESA compatible, or if you have loaded a VESA driver. Just for your information. ──Video Mode──────────────────────────────────────────────────────────── The current version of HOP supports up to 8 different video modes. In the initial video test that was performed after installation, HOP tried to find out which of the possible video modes are supported by your hardware and the video driver of your choice. The Video Mode popup menu contains only the supported modes, plus an option to repeat the initial video test (which you should do if your hardware changes). Each mode is described by three numbers (e.g. 320 x 200 x 256); the two first numbers stand for the horizontal and vertical resolution in pixels, and the third number stands for the maximum number of colors (usually 256). Generally, the highest resolution will look best. HOTKEYS= m / M = next higher / lower resolution alt-m = jump directly into this menu Resolutions above 640*480 are available in the registered version only. ──Show Values─────────────────────────────────────────────────────────── If this setting is ON, the screen will be split and all parameters of the current fractal will be displayed (with low resolutions, only a subset can be displayed) while the fractal will develop in a window. The complete color map that is currently used is shown in a vertical bar, with the current color indicated by a little horizontal bar. You can watch certain values change on their own and other values change as you press the corresponding hotkeys. Especially in the beginning, this can be very helpful. HOTKEYS= v = toggle Show Values screen ===================== HOP - Fractals in Motion ================= Page 42 ──Save Previous───────────────────────────────────────────────────────── If this setting is ON, the previous fractal will be saved to a special parameter file called PREVIOUS.HOP every time a fractal ends and a new one begins. There is a very short delay while HOP does this. Set 'Save Previous' to OFF if you are too impatient or if you want to run HOP from a writeprotected network server directory. Sometimes the random parameters will produce an incredible image, but because you are so enamored by the awe-inspiring effects of HOP, the screen clears and the next fractal starts before you press Ins to keep it. If Save Previous was ON, you can hit Backspace to recall your award-winning image. ──Keep on Change──────────────────────────────────────────────────────── When ON, if you change any value (e.g. you tried different colors or pressed the + zoom key), HOP thinks you like the current image. It will set the Maximum # of Pixels to zero, so that it will not end the fractal when it has reached its Maximum # of Pixels, but instead continue developing it until you end it explicitly by pressing the space bar. If Keep On Change is OFF, the fractal will end when it has reached its Maximum # of Pixels (unless you have explicitly told HOP to continue the current image by pressing Ins). ──Warning Beeps ─────────────────────────────────────────────────────── Late at night and you are the only one still awake, mesmerized by HOP? It is considered polite to switch the beeps off. ──Video Retrace───────────────────────────────────────────────────────── If your video screen flickers while the color palette is scrolled, you should experiment with this setting. If the flickering stays, you definitely need to get better video hardware. ──FadeoutTime (msec)──────────────────────────────────────────────────── If > 0, HOP will fade the fractal image to black when moving on to the next image. ──'Norton' Mouse──────────────────────────────────────────────────────── HOP employs a "graphics style" mouse cursor, similar to recent Norton products. This cursor style can cause odd effects when running under DESQview or other multitaskers. You can switch back to a boring block mouse cursor by setting this value to OFF. ──Image Save/Restore──────────────────────────────────────────────────── When ON, HOP will attempt to save the image before switching to the configuration screen. HOP will first try to save the image to the lower-memory heap, then to EMS memory, then to XMS memory, and finally to disk (if Save/Restore to Disk is ON). When returning from the configuration screen, the image will be restored (unless you have changed critical values in the configuration). If this setting is OFF, HOP will restart the fractal generation whenever you return from the text mode user interface. ===================== HOP - Fractals in Motion ================= Page 43 ──Save/Rest. to Disk──────────────────────────────────────────────────── If ON, HOP will use the hard drive as a last resort for saving the fractal image. Since this can be slow, you can turn this OFF if you would rather regenerate the image from scratch than have HOP save to the hard drive. (If you have sufficient EMS or XMS, HOP will use that and this setting will not matter.) ──Precomputing────────────────────────────────────────────────────────── A randomly generated fractal may be any size, and may be located anywhere on the screen. HOP will try to center the image and find the best magnification level. To do this, HOP computes the first few pixels of the new fractal before it actually draws them. This value controls how many pixels are precomputed. The higher the number of 'precomputed' values, the better the new fractal will fit on the screen, but the longer it will take before the image starts to draw. Default is 1000. ──Delay (msec)────────────────────────────────────────────────────────── In general, the faster the machine the better HOP runs, but as hardware advances HOP may run too quickly. Does your quad-processor, 200 MHz Pentium machine look like HOP on amphetamines? What a pity. Set a delay factor if you like. Pixels will pause for <delay> milliseconds, making the whole thing move at a slower pace. ──Titledisplay (msec)─────────────────────────────────────────────────── When displaying saved fractals from a .HOP file, the fractal titles will be displayed for <titledisplay> seconds, if you have specified -T+ on the command line, or Show Titles = ON on the Read page. ──Slideshow Delay (sec)───────────────────────────────────────────────── If you run HOP as a GIF image slideshow (this can be done from the Read page, or by specifying SLIDESHOW on the command line), this setting will determine how long a GIF image is displayed. ──Colorscroll Delay───────────────────────────────────────────────────── determines the speed of Static Colorscroll (see Color page) ──User Name───────────────────────────────────────────────────────────── You can exchange your fractal masterpieces with friends or on bulletin boards that are used by HOP enthusiasts. If you specify something here, it will be displayed on the titles along with the fractal names. ──GIF Image Dir───────────────────────────────────────────────────────── Specify something here if you have all your GIF images in a special directory. If you leave this field empty, they will be stored in (and read from) the current directory. ──Fractint MAP Dir────────────────────────────────────────────────────── Specify here where you store the Fractint fractal generator, or where you keep your Fractint color .MAP files (if they aren't in the current directory). HOP will look in the specified directory for the map files. ===================== HOP - Fractals in Motion ================= Page 44 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 7: READ FILE │ └────────────────────────────────────────────────────────────────────────┘ HOP can read three types of files: - HOP parameter files each of which can contain a number of parameter sets. A parameter set is very short (it is a text of about 20 lines) but it contains all information HOP needs to restore an image or animation, along with the title, author name, and the palette map that belongs to the image. Parameter files can be edited with any text editor if this should be necessary. They are similar to, but not compatible with Fractint PAR parameter files. For more details on HOP parameter files, see Appendix B. If HOP reads a parameter file, some things are different from its 'improvisation' mode: When you press the space bar (or PgUp/PgDn), the previous/next image in the specified parameter file will be displayed. HOP will stay in playback mode until you close the file by pressing F8. - GIF image files which can be static images created with HOP, or any other GIF image. Image files that you create with HOP contain information about the image in a parameter set which is stored in the image file. This parameter set can be run just as if it were contained in a HOP parameter file, so if you display a HOP GIF image, you get 1. the image itself and 2. the fractal as it reruns and grows until it looks like the saved image (or further). - Fractint type palette maps. They can be read from the Colors page. HOTKEYS= r = read something Pressing this hotkey will display the Read Page. After choosing filename, fractalname, etc., just press Enter to run the parameter file or display the image. Press F8 anytime to close the file. ──Read File Type ─────────────────────────────────────────────────────── Choose if you want to read a HOP parameter file, or a GIF file. ──Read Filename ──────────────────────────────────────────────────────── Choose the file name of the .HOP parameter file or of the GIF image file you want to play/display. Choose (All) if you want to play parameter sets from all .HOP files in your HOP directory, or if you want a GIF slideshow (which you can also do from the command line). ──Read Fractalname ───────────────────────────────────────────────────── Choose one of the fractals in the specified .HOP parameter file. Specify (All) if you want to see 'em all. Press f8 if you want to close the file and cancel the playback. ===================== HOP - Fractals in Motion ================= Page 45 ──Show Title ─────────────────────────────────────────────────────────── Specify if you want the fractal names (or GIF image file names) displayed. This corresponds to the -T command line switch (T+ is ON, T- is OFF). The setting you choose here will be remembered in HOP.INI and become the default value. ──Repeat──────────────────────────────────────────────────────────────── ON will repeat one fractal if you run one fractal, all fractals of the specified parameter file(s) if you chose (All), or the GIF slideshow. If OFF, you will be returned to the Read Page after playing/displaying if you started Read from here, or to the DOS prompt if you ran HOP in playback mode. This corresponds to the -R command line switch (R+ is ON, R- is OFF). The setting you choose here will be remembered in HOP.INI and become the default value. ──Rerun GIF───────────────────────────────────────────────────────────── If you display a GIF that was produced by HOP, the fractal parameters of the image will be read in from the GIF file. After displaying the GIF image, press a key to rerun the fractal from the start. ──Adjust Color Frequency──────────────────────────────────────────────── If the parameter sets you want to play back were designed on another computer, the color frequency values might be too slow or too fast for your computer's speed. If you have a very fast computer and the parameter sets were composed on a slow computer, the resulting fractals will scroll colors at a very high speed, too fast to look nice. If you have a slow computer and the fractals were designed on a fast computer, the colors might scroll so slowly that it takes seconds for each color and the resulting movement isn't smooth enough. If you set 'Adjust Color Frequency' to ON, HOP will ignore the values for Color Frequency and try to find a value that fits your computer's speed. This might or might not look better, but it will very likely change the look of the resulting image, so set this setting to ON only if really necessary. ===================== HOP - Fractals in Motion ================= Page 46 ┌────────────────────────────────────────────────────────────────────────┐ │ Page 8: SAVE FILE │ └────────────────────────────────────────────────────────────────────────┘ HOP can save data to three types of files: - HOP parameter files each of which can contain a number of parameter sets. A parameter set contains all information HOP needs to restore an image or animation. (see Page 7: Read File) - GIF image files. These contain one static HOP image and the information to reconstruct this image. - Fractint type palette maps. HOTKEYS= s = save something Pressing this hotkey will display the Save Page. After entering filenames, number of pixels, etc., press Enter to save. If you don't want to save, press the Tab key to highlight the 'Cancel' button instead of the 'Save' button, then press Enter (or click on the 'Cancel' button). ── From the Screensaver ────────────────────────────────────────────── 's' also works as a hotkey in HOP's screensaver module (HOPSVR.EXE) ! (All other keys will terminate program execution.) If you press this key from the screensaver, the current image will be saved to a parameter file called 'HOPSVR.HOP'. The incredible image that HOPSVR has just drawn won't be lost and can now be edited from HOP. ──Save File Type ─────────────────────────────────────────────────────── You can either save the current image parameters to a HOP parameter file, or save the current image to a GIF image file, or save the current color palette to a Fractint format MAP file. ──Save Filename ──────────────────────────────────────────────────────── Specify the name of the HOP parameter file that you want to save to. If the file exists, the current parameter set will be appended unless you choose to overwrite an existing parameter set. A HOP file can contain an unlimited number of parameter sets, but the larger a HOP file gets the longer it takes to read in. ──Save Fractalname ───────────────────────────────────────────────────── Specify a name for the current fractal. You have 16 characters. ──Pixels #────────────────────────────────────────────────────────────── Specify for how many pixels the saved fractal will develop when being played back. ===================== HOP - Fractals in Motion ================= Page 47 ──AutoGIFSave─────────────────────────────────────────────────────────── If you specify a GIF file name here, the current image will automatically be saved to a GIF file after being played back. The specified name will be the GIF file name. (The image will not be saved if a file with this name already exists.) This option can be used to make overlaid images, i.e. images that contain several fractals. Their parameter sets can be stored in one .HOP file; running the .HOP file will build up the overlaid image. The second fractal must use a GIF image of the first fractal as background, etc. ──Comment─────────────────────────────────────────────────────────────── Insert a comment here if the fractal needs to be saved with a comment. Also, the content of this line will be used as 'pixels' for HOP if the current pixeltype is 'Comment'. This will enable you to 'draw' with letters, words, and short sentences. If no comment has been entered and you have set 'Comment' as your pixeltype, a random combination of ascii characters will be used. ===================== HOP - Fractals in Motion ================= Page 48 ┌────────────────────────────────────────────────────────────────────────┐ │ GENERATE ANIMATION PARAMETERS (registered version only) │ └────────────────────────────────────────────────────────────────────────┘ One of HOP's rather experimental features is its ability to create a series of successive GIF images. This is simply done by generating a parameter file containing the parameter sets for each of the GIF images. (One starts out from an existing parameter set and sets values for various parameter changes from one image to the next. The rest is generated automatically.) The parameter sets contain values for 'AutoGIFSave'. Running the parameter file will then automatically generate the GIF images. What is a series of successive GIF images good for ? They can be used as input to an animation program like Dave Mason's DTA, or an Autodesk Animator program. These programs can generate .FLI animations from a series of single images. Such animations will resemble HOP's animated Hopalongs, but because fullscreen images can contain lots of detail, the resulting animation will look more interesting. Unfortunately, the Hopalong's tendency to 'hop' will make it difficult to produce really smooth successions of images. If someone manages to create a nice animation, I want to see it! This program feature can only be accessed from the command line. Enter HOP GENPARMS to start it. Choose the parameter set that will create the first image of the series. The second page contains a number of data fields, most of them containing the step sizes for several parameters as they change from one image to the next. Enter the values and choose Ok. The parameter file will be generated and you can run it later. ===================== HOP - Fractals in Motion ================= Page 49 ──No. of Images───────────────────────────────────────────────────────── Determine here how many parameter sets will be generated, i.e. how many GIF images will be created by HOP when running the generated parameter file. ──#Pixels per Image───────────────────────────────────────────────────── Each of the generated images will be saved to a GIF file after a certain number of pixels. ──.HOP filename───────────────────────────────────────────────────────── Enter the name of the .HOP parameter file that will now be generated as a basis for a series of GIF images. ──Zoom────────────────────────────────────────────────────────────────── If you enter a positive value here, the animation will zoom in just like the famous fractal zooms into the Mandelbrot set known from videos. Unfortunately, Hopalong fractals simply don't have an infinite depth. ──Horizontal Shift────────────────────────────────────────────────────── Consecutive images will move left or right if you enter a value here. ──Vertical Shift──────────────────────────────────────────────────────── Consecutive images will move up or down if you enter a value here. ──Rotate x,y,z────────────────────────────────────────────────────────── Consecutive images will rotate along the x, y, and z axis if you enter values here. ──Transform───────────────────────────────────────────────────────────── Consecutive images when being played back with an animation program will change shapes just like in a HOP animation when you enter a value here. This value is probably the most interesting for animations. Be careful to choose small enough values to make the movement as smooth as possible. You won't manage to make it *real* smooth though - this seems to lie in the nature of Hopalong fractals. ──Color Shift─────────────────────────────────────────────────────────── If you enter a value here, the color palette will scroll as consecutive images will be displayed in the animation. ===================== HOP - Fractals in Motion ================= Page 50 ┌────────────────────────────────────────────────────────────────────────┐ │ HOTKEY LIST │ └────────────────────────────────────────────────────────────────────────┘ As soon as you press one of the hotkeys that affects the image (or change values on the data entry screens) the current image will be kept and not be replaced by another image (unless you have set 'Keep On Change' to OFF). You can also press the Insert key to make the current image stay if you like it. Now the current fractal can be tailored until it is good enough for storing in a HOP parameter file. When you are tired of the current image, press the space bar or PgDn, and a new image will come up. Hotkeys that toggle a setting will beep high when the new value is ON and low when the new value is OFF. Many hotkeys are case sensitive ! ('c' and 'C' will have quite different results). Note that for a 'Pattern Only' formula, many hotkeys won't have any effect. The following overview can be displayed directly from the graphics screen by pressing F1. General Hotkeys ───────────┬─────────────────────────────────────────────────────────── esc │ exits to DOS enter │ loads user interface f1 │ display hotkey list f2 │ display current parameter set space bar │ ends the current fractal and starts next pgup/pgdn │ previous/next fractal backspace │ previous fractal ^backspace │ undo all changes ins │ keeps fractal │ r │ read parameter file / GIF image s │ save parameter file / GIF image / color map f8 │ close parameter file │ f9 │ truncate beginning of fractal f10 │ refresh/redraw with new random seed home │ refresh/redraw │ v │ 'Show Values' screen m/M │ next higher/lower videomode @m │ choose videomode ===================== HOP - Fractals in Motion ================= Page 51 Fractal Values / Math Effects ───────────┬─────────────────────────────────────────────────────────── f/F │ next / previous formula * │ random values for formula constants │ cursor keys│ move fractal # │ re-center image +/- │ zoom in/out │ ^pgup │ change rotation angles ^r │ toggle rotate │ n/N │ show every nth pixel: increment / decrement n ^n │ show every pixel │ ^t │ toggle transform effect t/T │ increment / decrement transform factor @t │ random transform factor │ a │ toggle animation @a │ toggle animation rotate > < │ animate direction │ k │ toggle warp effect type (spirals/eyes) K │ no warp effect ctrl-k │ set a random value for warp frequency alt-k │ set a random value for warp depth │ @f1 │ set animation type = Slow Changes @f2 │ set animation type = Fast Changes @f3 │ set animation type = Lines @f4 │ set animation type = Dancing Beads @f5 │ set animation type = Kaleidoscope │ f7 │ synchronize erase queue length 'e' │ with transform frame length 'f' │ and color frequency 'c' f5 │ decrement efc f6 │ increment efc shift-f5 │ decrement efc by efc/2 shift-f6 │ increment efc by efc/2 ^f5 │ set efc = 1 ^f6 │ set efc = max ===================== HOP - Fractals in Motion ================= Page 52 Graphic Effects ───────────┬─────────────────────────────────────────────────────────── d/D │ next / previous black-white pattern ^d │ no background pattern │ @1 │ pattern = plasma @2 │ === connett circle @3 │ === rings @4 │ === squares @5 │ === horizontal lines @6 │ === vertical lines @7 │ === wheel │ w │ toggle 'Erase oldest Pixels' │ x/X │ next / previous pixel type @x │ pixeltype = pixel ^x │ no pixels q │ toggle elliptic pixelshape i/I │ increment / decrement pixelsize @i │ set pixelsize = 1 ^i │ toggle oscillate │ z/Z │ next / previous pixel fillpattern ^z │ pixel fillpattern = solidfill │ ^q │ toggle pixel reflection @q │ toggle pixel border │ y/Y │ next / previous symmetry ^y │ no symmetry │ l │ toggle connect = colored lines L │ toggle connect = conditional lines @l │ toggle connect = background color lines ^l │ toggle connect = 'no erase' lines / │ line thickness j │ toggle linestyle = solid/dotted │ o │ toggle shadow type (background/always) O │ no shadow │ . │ toggle twinkle g/G │ next / previous grid ^g │ no grid ===================== HOP - Fractals in Motion ================= Page 53 Color Hotkeys ───────────┬─────────────────────────────────────────────────────────── e │ edit palette b/B │ colored/black backgrd │ 0-9 │ color frequency (0 = 1, 9 = 1000) shift- │ decrement/increment color frequency shift-left/right scroll one color left/right │ h/H │ increment/decrement color mapping type │ C │ tie colors │ P │ periodic palette p │ irregular palette @p │ continuous palette \ │ add contrast color stripes ^p/^P │ load next/previous color MAP palette │ c │ toggle colorscroll u │ toggle color pulsating ^c │ scroll direction │ @c │ toggle static colorscroll ===================== HOP - Fractals in Motion ================= Page 54 ┌────────────────────────────────────────────────────────────────────────┐ │ COMMAND LINE PARAMETERS │ └────────────────────────────────────────────────────────────────────────┘ Brackets [] indicate that these parameters are optional: HOP [filename [#n]] [RANDOMPLAY] [/R[+|-]] [/T[+|-]] [/C[+|-]] [SLIDESHOW [GIF filenames]] [GENPARMS] [PASSWORD] [REGISTER] [UNREGISTER] ┌─────────────────────────────────────────────────────────────────┬──────┐ │ Command Line │Screen│ │ Parameter │saver │ ├─────────────┬───────────────────────────────────────────────────┼──────┤ │ filename │ must be a valid .HOP parameter filename │ √ │ │ │ (wildcards can be used). The parameters │ │ │ │ contained in the specified file(s) will be │ │ │ │ played back. │ │ │ │ The filename can also be a GIF filename (wild- │ │ │ │ cards can be used) but .HOP parameter files │ │ │ │ are default. If you issue HOP BLAH on the │ │ │ │ command line, HOP will look for a BLAH.HOP │ │ │ │ parameter file. If there is no file with this │ │ │ │ name, it will look for a file called BLAH.GIF. │ │ │ │ If no GIF file of this name can be found, there │ │ │ │ will be an error message that BLAH.HOP could │ │ │ │ not be found. │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ #n │ is the number of a specific parameter set that │ √ │ │ │ is to be played back (e.g. HOP EXAMPLE #3). │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ RANDOMPLAY │ will play parameter sets in the specified file │ √ │ │ │ in random order. When no filename is specified, │ │ │ │ all parameter files in the current directory │ │ │ │ will be played back in random order. │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ /R+ │ will play back the parameter sets in an endless │ - │ │ │ loop (corresponds to the Repeat option on the │ │ │ │ Read page). │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ /T+ │ will display the parameter set titles (corres- │ - │ │ │ ponds to the Titledisplay option). │ │ ===================== HOP - Fractals in Motion ================= Page 55 ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ /C+ │ will ignore the color frequency value of the │ √ │ │ │ parameter file and instead set it to a smooth │ │ │ │ value for your PC's speed. This will change the │ │ │ │ look of the resulting image ! │ │ │ │ (corresponds to 'Adjust Color Frequency') │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ SLIDESHOW │ will run a GIF image slideshow (/R and /T also │ - │ │ │ apply here). 'Slideshow' is an optional parameter│ │ │ │ (you can omit it if you issue GIF filenames │ │ │ │ that cannot be misunderstood as HOP parameter │ │ │ │ filenames). │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ GIF │ are GIF filename wildcards │ - │ │ filenames │ (e.g. HOP SLIDESHOW ANI*.GIF). │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ GENPARMS │ (Generate Animation Parameters) │ - │ │ │ will generate a series of parameter sets which │ │ │ │ will create a series of GIF files when being │ │ │ │ played back. These GIF files can then be used as │ │ │ │ input for an animation program. │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ PASSWORD │ can be used to set, delete, or modify a password │ - │ │ │ for the screensaver (DOS only). │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ REGISTER │ must be specified when you want to register HOP. │ - │ │ │ You will receive information about this feature │ │ │ │ when you contact one of the authors to register │ │ │ │ HOP. │ │ ├─────────────┼───────────────────────────────────────────────────┼──────┤ │ UNREGISTER │ can be used to unregister a previously │ - │ │ │ registered copy. │ │ └─────────────┴───────────────────────────────────────────────────┴──────┘ ===================== HOP - Fractals in Motion ================= Page 56 ┌────────────────────────────────────────────────────────────────────────┐ │ TROUBLESHOOTING / FREQUENTLY ASKED QUESTIONS │ └────────────────────────────────────────────────────────────────────────┘ Q: HOP aborts with a runtime error message, hangs your computer, or does other things that just shouldn't happen. A: Sorry. Any critical runtime error will abort program execution and generate a file called ERRORS.HOP which contains an error protocol. You can help make HOP better by emailing this file to one of the authors. Even if no runtime error occurs, there may still be bugs in the program (programmers insist on the saying that 'there is no program without bugs'), or you think that HOP behaves strangely under certain circumstances. Sending us error reports and any kind of criticism will help make the next version better. Please don't forget to describe your hard/software configuration (available memory shown by MEM etc) when you send something. Q: Why can't one do (this and that)? Q: Because I had to stop at a certain point, or else HOP would never have been released. New ideas for the program kept coming along all the time. There's a number of new features that I didn't include because I finally wanted to release the program. If HOP has a certain degree of success, there will certainly be a next version with more features, a better logic, and less bugs. Q: Isn't (this particular logic or menu structure) a little chaotic ? A: Parts of the program could certainly be structured much more intuitively and logically (mainly because some new features came along at a point of development when the program was almost ready), but then I didn't want to do a major redesign of the menus and the logic because I wanted to finally complete the program. Let's all hope for a next version. Q: Why does HOP have a text mode interface and hotkeys instead of a graphical interface and full mouse support? A: A graphical user interface for DOS was difficult to write, and would have slowed down performance considerably. Versions for OS/2 and Windows are planned, but of course the realization largely depends on your support (i.e., registering! <g>). Q: The screen flickers most of the time when the colors are scrolled. What can I do? A: Check if changing the 'Video Retrace' configuration setting makes a difference. If not, you can either tune Colorscroll % to zero (which will be a loss), or buy a better video card with more memory. If you run HOP under OS/2, try changing the DOS session video settings. If the only video mode you can use is 16 color EGA, there is nothing you can do except getting better video hardware. Q: I switched a lot between the different pages, and now the image seems to contain some garble. A: Press [home] to redraw the current image. ===================== HOP - Fractals in Motion ================= Page 57 Q: Everything is running extremely slowly ... A: Do you have a mathematical coprocessor or a 486 (or above)? If not, you should definitely get one. If you have a fast enough machine, it seems you have chosen a combination of very 'slow' special effects (e.g. if Thick Lines is set ON, this will slow down everything that has to do with line drawing, including circles). Q: After the initial video check, only cheap VGA (320*200) and EGA are working ok. I know that my video equipment can do better than that ! Why doesn't HOP run with higher resolutions ? A: It seems that you need a VESA driver for HOP. Ask your hardware dealer for a VESA driver disk, then load the driver and rerun the video check ( = just delete HOP.INI and rerun HOP). Q: Some example parameter sets that came with HOP (or from other HOP users) seem to run too slowly. Pixels and scrolling colors aren't really moving smoothly. Or: everything runs too fast and the colors scroll so fast that it makes me nervous. A: Your machine runs slower or faster than the machine that these parameter sets were designed on. Try setting 'Adjust Color Frequency' to ON on the Read Page, or add a /C+ on the command line. This will change the look of the fractal, but at least it won't make you nervous. Q: The screen is completely blank! What has happened? A: You have either lost the fractal (it is somewhere outside the screen), or you have set Pixelshape to None, or there are Background Color lines in combination with Pixelshape = None or = Pixel, or formula is set to '(Pattern)' and no background image or pattern was chosen. If the fractal is off the screen, either press the # key several times until the fractal comes back into the visible area, or press a cursor key. This will display rectangles which symbolize screen and fractal position. Press cursor / ctrl- cursor keys to move the fractal rectangle back into the center. If Pixelshape is the problem, try hitting x to change it. If nothing at all helps, HOP hangs and we have a problem. Q: I want to print HOP images. Why is there no print option? A: This would have blown up the code unnecessarily. If you want to print an image, save it to GIF and use one of the many GIF printing tools that are available. If you don't like the GIF format, there are dozens of programs that convert GIF into PCX, BMP or others. Q: The screensaver doesn't run. It keeps saying 'This seems to be a PC that HOP hasn't run on before', etc. What am I supposed to do ? A: You must have configured HOP for your machine. (The file HOP.INI must have originated on your machine. If in doubt, delete HOP.INI and rerun HOP.) If the message continues to appear, this is probably because you moved HOPSVR.EXE (and maybe other files) to a different harddisk, making HOP think this is a new computer. If this is the case, 1. be sure to copy *all* HOP files to the new destination, 2. delete the relocated HOP.INI and 3. rerun HOP from the new directory - this will start a reconfiguration and a new HOP.INI. This should take care of the problem. ===================== HOP - Fractals in Motion ================= Page 58 Q: I want to use HOP commercially. Is that ok? A: Whatever you do, please register (see below). If you have a computer shop, we ask you to run Hop in your shop window and to distribute the unregistered version of HOP. If you plan other commercial applications, please don't do it without written permission. Why don't you write us a message so we can try to find a satisfactory solution. This also applies to company registrations and site licenses. If you are interested in having a customized screensaver written by us, please contact one of the authors (see addresses below). If you plan to use HOPTSR.EXE (the program that works as a screensaver shell for HOPSVR.EXE) commercially, please contact Andy Cramer (see Screensaver chapter). ┌────────────────────────────────────────────────────────────────────────┐ │ DISCLAIMER │ └────────────────────────────────────────────────────────────────────────┘ The authors assume no responsibility for any damage or loss caused by the use of this program. THIS PROGRAM IS PROVIDED AS IS WITHOUT ANY WARRANTY, EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO FITNESS FOR A PARTICULAR PURPOSE. ┌────────────────────────────────────────────────────────────────────────┐ │ REGISTERING │ └────────────────────────────────────────────────────────────────────────┘ HOP is distributed as shareware. This means: you get it for free, but if you like HOP, use it a lot and have fun with it (or even use it commercially), you are asked to register. Registration fee is US$ 30 (Britain: £ 20) (Germany: DM 48). To register, just send a message saying 'HOP Registration' (including your full address and the fee) to one of the authors: ┌──────────────────────────────────────────────────────────────────────┐ │ Michael Peters, HOP Software, Postfach 600645, 50686 Koeln, Germany │ │ │ Compuserve: 100041,247 │ │ Internet: mpeters@ibm.net │ │ or m.peters@link-lev.cl.sub.de (in Germany) │ │ Send Eurocheques or other cheques that are valid in Germany, or │ │ pay to: Postscheckkonto 2271 41-507, PostGiro Koeln, BLZ 370 100 50 │ │ └──────────────────────────────────────────────────────────────────────┘ or ┌──────────────────────────────────────────────────────────────────────┐ │ Randall Scott, 1013 Mondale Lp., Las Cruces, NM 88005, USA │ │ Compuserve : 72002,2746 │ │ Internet : rascott@nmsu.edu │ │ Fidonet : 1:305/102 │ │ World Wide Web: http://rever.nmsu.edu/~ras/ │ │ │ │ Send cheques that are valid in the USA. │ └──────────────────────────────────────────────────────────────────────┘ ===================== HOP - Fractals in Motion ================= Page 59 If you are a member of Compuserve, simply use the Compuserve Shareware Registration Service (GO SWREG). HOP's ID number is 3253. Credit card payment directly to the authors is not possible. There is a discount for subscribers of FRAC'cetera (see page 63). On registering, you will receive a code number which will switch on some additional goodies: > higher SuperVGA resolutions (up to 1024*768 with 256 colors) which will make your creations look even more brilliant > tuning options to give you control over HOP's random decisions > a palette editor to design your own 256 color palettes > an option to generate animation parameter files which can produce series of GIF images as input for FLI type animations > a password option for the screensaver (DOS only). If you have already registered HOP ================================== In this case we ask you not to give away your own registered copy. Please do only give away copies of your original copy of HOPZIP.EXE (a compressed file which should contain an unregistered copy of HOP.EXE). If you haven't received HOP as a compressed HOPZIP file but as a collection of single files, please do the following: - Copy all files from your HOP directory (at least the files from the list on page 4) to an empty floppy disk. - Delete your HOP.INI from the floppy disk (this is a configuration file which shouldn't be distributed because it could lead to problems on PCs with a hardware different from yours). - If there are HOP screensaver files (HOPSVR.*) in your Windows directory, copy these to the floppy disk. - Change to the floppy disk by typing A: or B: depending on the disk drive you use. - Unregister the new copy by entering HOP UNREGISTER. - Return to your hard drive by typing C: (or whatever your hard drive is). - You can now distribute the floppy disk. Thanks for your cooperation. ===================== HOP - Fractals in Motion ================= Page 60 ┌────────────────────────────────────────────────────────────────────────┐ │ DISTRIBUTION │ └────────────────────────────────────────────────────────────────────────┘ As the sole copyright holders of HOP, Michael Peters and Randall Scott reserve all rights to the program. However, the shareware version of HOP may be freely distributed by commercial vendors, user groups, BBS operators, or individuals, with the following restrictions: - HOP must be distributed in unmodified form in its entirety, including all files that are listed in the FILES chapter of this documentation. No other programs or files may be included (except additional parameter file collections). The files may be distributed in a compressed or library format. - Copies of HOP may only be distributed if they are unregistered (i.e. if HOP's intro screen says "unregistered shareware version"). - HOP may not be included in combination with any other software or hardware product as an enticement or for any other reason, without special permission from the authors. - No fee or payment may be charged or accepted for HOP, other than a small disk distribution fee. - HOP cannot be rented or leased. - HOP may not be packaged or distributed with any of its supporting documentation pre-printed for the end-user. - HOP may not be described in catalogs or promotional material as "public domain" or "free" software. - Any advertising and/or packaging must explain the shareware concept and the obligations associated with continued use of shareware. Commercial vendors who wish to distribute HOP should contact HOP's authors to ensure that they have the latest version. Contact one of the authors for details on site licenses. ===================== HOP - Fractals in Motion ================= Page 61 ┌────────────────────────────────────────────────────────────────────────┐ │ SUPPORT / CONTACT │ └────────────────────────────────────────────────────────────────────────┘ If you have questions, problems, comments, or suggestions, please contact one of the authors (email addresses: see above), or send them to HOP's mail list on the Internet. The development of the next version depends on your feedback ! New versions of HOP are available at the following sites. New versions will be available first, and more or less simultaneously, by FTP at rever.nmsu.edu, by World Wide Web at http://rever.nmsu.edu/~ras/hop, and by BBS at Fidonet 1:305/101 (505-646-2868). Look for HOPxxx.ZIP in all cases. (xxx represents the version; i.e., HOP120.ZIP is version 1.2.) Major upgrades will be available on Compuserve as well. FTP --- HOP also has its own anonymous FTP site. To access it, FTP to rever.nmsu.edu. The latest version of HOP, along with other HOP-related stuff, can be found in /pub/hop. You can always find the latest version of HOP at this location. World Wide Web server --------------------- HOP has its own "Home page" on the World Wide Web. To access it, point your WWW browser to http://rever.nmsu.edu/~ras/hop You can always find the latest version of HOP (as well as images and HOP parameter files) at this location. BBS --- HOP can also be found at the NASW BBS (505-646-2868), in File Area #1. Downloads are available on the first call. V.32bis (14,400 bps) and lower speeds are supported. Fidonet file-requests are supported (Fidonet node 1:305/101). In Germany, HOP can be found at the LINK-LEV BBS (0214-77359) in area BINAER/IBM/FRACT (Username/Password is GAST). Compuserve ---------- GO GRAPHDEV (section 4: Fractal Sources). This forum contains the latest versions of HOP, images, and parameter files. You can also send comments and questions here. ===================== HOP - Fractals in Motion ================= Page 62 HOP Internet mail list ------------------------- The HOP mail list is available for both registered and unregistered HOP users. It is open for discussion of any HOP-related topic. Subscriptions and info requests for the HOP mail list should be sent to: hop-request@acca.nmsu.edu To subscribe to the HOP mail list, simply send a message with the word "subscribe" in the Subject: field. For information, send a message with the word "INFO" in the Subject: field. Note that since the HOP mail list is based on email it is available to non-Internet users through CompuServe, America OnLine, Prodigy, etc. Any on-line service that can send and receive email to the Internet can access this mail list. (Note that some services, such as CompuServe, charge for both incoming and outgoing Internet email.) ┌────────────────────────────────────────────────────────────────────────┐ │ COPYRIGHTS │ └────────────────────────────────────────────────────────────────────────┘ HOP HOP - FRACTALS IN MOTION HOPSVR are Copyright (c) by Michael Peters and Randall Scott HOPTSR.EXE and HOPSVR.SCR Copyright (c) Andrew Cramer GIF The Graphics Interchange Format(c) is the copyright property of CompuServe Incorporated. GIF(sm) is a Service Mark property of CompuServe Incorporated. LHA Copyright (c) Haruyasu Yoshizaki, 1988-91 ===================== HOP - Fractals in Motion ================= Page 63 ┌────────────────────────────────────────────────────────────────────────┐ │ RELATED PRODUCTS │ └────────────────────────────────────────────────────────────────────────┘ FractInt is *the* fractal generator for Mandelbrot and Julia sets and dozens of other fractal types. It was written by members of the Stone Soup Group (SSG) and is available in the Compuserve GRAPHDEV forum for free! If you like fractals and haven't heard of Fractint, this is a must. Fractint itself and the Graphdev forum are also a valuable source for many beautiful color map files which can be used in HOP. FRAC'Cetera is a fractal newsletter on diskette, containing information on fractals and related matters, shareware, books, CD-ROMs, videos, FRUG - The Fractint User Group, etc. Current versions of Fractint and HOP always available. For information, contact: Jon Horner, FRAC'Cetera, Le Mont Ardaine, Rue des Ardaines, St.Peters, Guernsey GY7 9EU, CI, UK. Phone (44) 0481 63689 CIS: 100112,1700 Subscribers of FRAC'cetera can register HOP for US$ 20 instead of US$ 30 (£ 14 instead of £ 20; DM 32 instead of DM 48) ! ┌────────────────────────────────────────────────────────────────────────┐ │ CREDITS │ └────────────────────────────────────────────────────────────────────────┘ Barry Martin 'invented' (or rather: discovered) Hopalong fractals. Barry is from Aston University, Birmingham/England. A.K.Dewdney wrote the 'Wallpapers for the Mind' article about Barry's fractals in the 9/1986 issue of Scientific American. ──────────────────── Hop includes software from ──────────────────────── Andrew Cramer [70670,3620] [aic@world.std.com] wrote the HOPTSR screensaver shell program for DOS and Windows (for more information read the screensaver section of this manual) Bob Berry [76555,167] and Rob Crockett [76167,1561] wrote the GIF encoding module Michael Day [70007,4645] wrote the VESA compatible SuperVGA drivers Jordan Hargrave [72510,1143] wrote the SuperVGA drivers that run Hop on VESA incompatible systems Dave Kirsch [zoid@cc.sfu.ca] designed the 'Norton' style mouse cursor D. J. Murdoch [72537,1154] translated Dave Kirsch's C code into Pascal Tim Wegner [71320,675] modified Bret Mulvey's Plasma algorithm Sean Wenzel [71736,1245] wrote the GIF decoding module ===================== HOP - Fractals in Motion ================= Page 64 ───────────────────────────── Coauthors ──────────────────────────────── Randy Scott [Compuserve: 72002,2746] [Internet: rascott@nmsu.edu] [Fidonet: 1:305/102] contributed image save/restore routines, the help system, the palette editor, the registration mechanism ... and countless other parts of the HOP machinery. He also helped to shape the general program architecture. Simon Walker [100026,1137] contributed EGA routines, 3-D geometry, and invaluable moral support in HOP's early days. ─────────────────────────── Programming help ─────────────────────────── Thanks to Juan Jimenez, Pat Ritchey, J.W. Rider, K. Barthelmess, John Leier, Neil J. Rubenking, Paul Andre LeBlanc, Steve Schafer, Charlie Calvert, Kim Kokkonen, Scott Bussinger, D.W.Mitchell, and Michael Day (from Compuserve's BPASCAL forum and the TeamB group). ──────────────────────────── and finally ... ─────────────────────────── thanks to Sabine Schachtner for love and patience Christiane Eichler, Jon Horner, Ted Hudek for beta testing and manual proofreading Norbert Meder and Lisa Lang for time, money, and hardware Olaf Koch for turning me on to the 'Net' Brian Eno, Robert Fripp, Jon Hassell, Michel Redolfi, Steve Reich, Philip Glass, La Monte Young, Marian Zazeela, Michael McNabb, The Orb, Future Sound of London, and many others ... for sounds and visions ===================== HOP - Fractals in Motion ================= Page 65 ┌────────────────────────────────────────────────────────────────────────┐ │ APPENDIX A: Configuration file HOP.INI │ └────────────────────────────────────────────────────────────────────────┘ HOP.INI contains all configuration and tuning values for HOP. HOP.INI can be edited manually but please be careful to enter valid values only, otherwise the program might react in an unpredictable way. HOP.INI name Name in user interface Other ─────────────── ────────────────────── ─────────────────────────── colfreqadjust Adjust Color Frequency delayall Delay disksave Save/Rest. to Disk fadeouttime FadeoutTime gifdelay Slideshow Delay gifdir GIF Image Dir help - ON if help page was displayed hdid - harddisk ID (video config is invalid if this has changed) keeponchange Keep on Change mapdir Fractint MAP Dir mapno - # of MAP file last read nortonmouse 'Norton' Mouse password encrypted password for the screensaver precompute Precomputing repeatplayback Repeat (when reading) rerungif Rerun GIF saveprevious Save Previous saverestore Image Save/Restore scrolldelay Colorscroll Delay showtitles Show Title (when reading) showvar Show Values sound Warning Beeps titledisplay Titledisplay username User Name videomode Video Mode videook - -1=bad, 0=unchecked, 1=good for each of the 8 possible modes videoretrace Video Retrace windir directory for HOPSVR.PIF and .SCR ===================== HOP - Fractals in Motion ================= Page 66 Tuning settings in HOP.INI: HOP.INI name Name in user interface ─────────────── ────────────────────── avgmaxcount φ No. of Pixels density Density transform Transform animation Animation patterns Patterns Only warp Warp Effects shadow Shadows rotation Rotation symmetry Symmetry slowpix Slow Pixels colorscroll Colorscroll black Black Background slowchanges (Tuning values for animation) fastchanges " lines " dancingbeads " kaleidoscope " periodic (Tuning values for palette types) irregular " map " continuous " ===================== HOP - Fractals in Motion ================= Page 67 ┌────────────────────────────────────────────────────────────────────────┐ │ APPENDIX B: *.HOP parameter files │ └────────────────────────────────────────────────────────────────────────┘ *.HOP files contain one or several parameter sets, each describing a HOP fractal. Parameter files can be edited manually, but please be careful to enter valid values only, otherwise the program might react in an unpredictable way. At any rate, do not modify the first line of the parameter set. While HOP draws a fractal, you can display the current parameter set by pressing F2. Structure of a parameter set: - a ';' character in the first row indicates a comment - a parameter set begins with a 16-character name and ends with a '}' character - the first line contains the name and (beginning with a '{' character in column 18): 1. a HOP version number, 2. the author's name and 3. the creation date, each separated by a '∙' character - the second line can contain a comment, beginning with a ';' character in column 20 - parameters begin with the parameter name. If a parameter name cannot be identified by HOP, it is ignored. Parameters that are not specified are set to their default values. There is no fixed parameter order. - The color description consists of 256 sets of 3 characters (the RGB values). A value of 60 is added to each RGB value; the resulting number is represented as the corresponding ascii character. (A color with RGB values 0,0,0 is represented as "<<<" .) To save some storage space, parameter names are often abbreviated. Here's a concordance to show you what they mean. If on the pages of the user interface, a value is chosen from a menu and then represented as a text string, it is often represented as a number value in the parameter set. In most cases, this number stands for the menu position of the value. parameter name Name in user interface ─────────────── ────────────────────── a a autogifsave autogifsave b b bor pixel border bwpat black/white background pattern c c colcnt color frequency colfwd colorscroll upward colmap color mapping colordiv color divide at colpulse pulsating colors connect connect lines conseed connett circle seed cpat color pattern (a 7 char series of either -, x, or o) ===================== HOP - Fractals in Motion ================= Page 68 parameter name Name in user interface ─────────────── ────────────────────── d d ell elliptic pixels everynth show every nth pixel formula formula frame frame length fwd forward transform motion gifbk gif background image name grid grid ltype solid or dotted lines map palette map name movie animation osc pixel oscillate palmode palette mode pixels max pixels pixfill pixel fill type pixshape pixel shape pixsize pixel size plasma plasma seed plassym plasma symmetry plasovl plasma overlay random base random ref pixel reflection rot rotation rotframes rotate animation rotfrate rotate animation speed scr1 colorscroll from scr2 colorscroll to scroll colorscroll shadow shadow shx shadow x distance shy shadow y distance warp warp effect wdepth warp depth wfreq warp frequency sscroll static scroll starttf transform factor sym symmmetry tf transform effect tfinc animation speed thick thick lines tiecol colors tied twinkle twinkle frequency wipe erase queue wipecnt erase queue length x x xrot rotation x-axis y y yrot rotation y-axis zoom zoom zrot rotation z-axis ===================== HOP - Fractals in Motion ================= Page 69 ┌────────────────────────────────────────────────────────────────────────┐ │ APPENDIX C: The Hopalong algorithm │ └────────────────────────────────────────────────────────────────────────┘ For those of you who want to do their own experimenting, here's a simple Hopalong program written in Turbo Pascal. (You need GRAPH.TPU and EGAVGA.BGI to run it.) The user interface works like this: Press Esc to leave the program; press any other key to display a new fractal. {╔═════════════════════════════════════════════════════════════════════╗} {║} program Hopalong; {║} {║} uses graph, crt; {║} {║} var driver, mode, mx, my : integer; {║} {║} maxcolor : word; {║} {║} q : char; {║} {║} x, y, xn, a, b, c : real; {║} {║} {║} {║} function sgn(s:real):real; {║} {║} begin {║} {║} if s < 0 then {║} {║} sgn:= -1 {║} {║} else if s = 0 then {║} {║} sgn:= 0 {║} {║} else {║} {║} sgn:= 1 {║} {║} end; {║} {║} {║} {║} begin {║} {║} driver:= EGA; mode:= EGAHi; {║} {║} initgraph(driver, mode, ''); {║} {║} maxcolor:= getmaxcolor; {║} {║} mx:= round(getmaxx / 2); {║} {║} my:= round(getmaxy / 2); {║} {║} randomize; {║} {║} repeat {║} {║} x:= 0; y:= 0; {║} {║} a:= random(100) + 1; {║} {║} b:= random(100) + 1; {║} {║} c:= random(100) + 1; {║} {║} repeat {║} {║} {'Classic' Hopalong formula :} {║} {║} xn:= y - sgn(x) * sqrt(abs(b * x - c)); {║} {║} y:= a - x; {║} {║} x:= xn; {║} {║} putpixel(round(x) + mx, {║} {║} round(y) + my, {║} {║} random(maxcolor)) {║} {║} until keypressed; {║} {║} q:= readkey; {║} {║} cleardevice; {║} {║} until q = #27; {║} {║} closegraph; {║} {║} end. {║} {╚═════════════════════════════════════════════════════════════════════╝} ===================== HOP - Fractals in Motion ================= Page 70 Martin's 'classic' formula needs three constants a, b, and c which can be set to any value between -100 and 100 (except zero) for interesting results. The variables x and y contain the screen coordinates for a pixel. The value of the 'sign' function is -1 for a negative x and 1 for a positive x. The algorithm simply takes the position values (x,y) of the previous pixel (for the first pixel, they are 0,0) and inputs them into the formula. The result of the formula calculation is the position of the next pixel. The new pixel is drawn and its new position values are again used as input for the formula, and so on. ===================== HOP - Fractals in Motion ================= Page 71 ┌────────────────────────────────────────────────────────────────────────┐ │ APPENDIX D: QUICK TUTORIAL │ └────────────────────────────────────────────────────────────────────────┘ To get an idea how to use HOP, you can read this short tutorial and follow its instructions. (You must have printed out the manual first of course.) 'Tutorial' doesn't mean that you'll be a HOP specialist after reading this - it is just a suggestion for how to begin. The tutorial requires that HOP has been correctly configured for your PC video hardware and that all other configuration items are set to default values. If you are not sure if this is the case, leave HOP, delete the file HOP.INI, and restart HOP. What we'll do is take an image from HOP's demo and turn it into something completely different. 1. From the DOS prompt, enter HOP DEMO #24 Wait until HOP has loaded the demo file and started drawing fractal #24 which is called 'Classic Hopalong' (unless somebody has modified the DEMO.HOP file). This fractal gets its shape from the 'classic' Hopalong formula, but to make it look a little more interesting, it is drawn with little blue bubbles which have an line pattern internal structure, a white dot which looks like a light reflection, and shadows. 2. First press the v key. This will divide the screen into a vertical column of parameters and a graphics window for the fractal. This 'Show Values' screen is helpful because it shows you the current value of most parameters as well as the current color palette as a whole. The 'Show Values' screen should be ON for the time of the tutorial. Look up the value of 'Maxpixels'. It should be 30000. This is the number of pixels that HOP will draw for this fractal; after 30000 pixels it will start a new image. 3. Press p, P, alt-p, and ctrl-p several times. This will set new color palettes. The various 'p' key combinations stand for different algorithms that generate palettes with different characteristics. If Fractint Map files are present in the current directory, ctrl-p loads the next map file. The 'Show Values' screen contains a vertical color bar that contains all 255 colors of the current palette, as well as a little line wandering along it. The line points to the current drawing color. Choose a color palette that you like, or press ctrl-backspace to return the image to its original look and the blue-orange on black. ===================== HOP - Fractals in Motion ================= Page 72 The value of 'Maxpixels' should have changed to zero when you started changing the image. HOP thinks you like the current image because you played with it, so it set Maxpixels to 0 (unlimited). 4. Play with the Colorscroll feature: Press c to switch it on. Reverse the scroll direction by pressing ctrl-c. Press the shift key together with cursor-up and cursor-down to accelerate/decelerate Colorscroll speed. Add HOP's Colorpulsate effect by pressing u. The fractal continues to grow while the colors scroll. 5. Switch on Static Colorscroll by pressing alt-c. Watch how the colors scroll but the fractal doesn't grow at the same time. Switch it off again by pressing alt-c. Press u to switch off Colorpulsate, and press c to switch off Colorscroll. 6. Let's play with the look of the bubble pixels. If you haven't turned on the Showvar screen, press v until you see a vertical row of parameter names. Press q. The image will be redrawn with pixels that have an elliptic shape instead of a circle shape. Press ctrl-z to reset the fill pattern from a 'diagonal line' fill to 'solid' fill. Press (small) b until the background has a color different from black. Press alt-q. The bubbles have a black outline now. Press ctrl-q. This will switch off the white dots which look like light reflections. 7. In HOP, a pixel can be represented in various ways. There are about ten pixel shapes available. (The current shape which looks like bubbles is called 'Pixel/Circle'). Most of them are scalable, and most of them have various properties (e.g. an elliptic shape, a reflection, a fill pattern, or an outline). Each of these properties can be switched on and off. Press x several times. This will turn the bubbles into rectangles, then into triangles, next into triangles with a more geometric order, next into lines that form a structure like pins in a magnetic field, next into little flakes and fuzzy things, and then into several other shapes that are hard to describe. Each of these pixel shapes has a unique character. Together with the pixel 'properties' mentioned before, dozens of different designs are possible. Press x until you return to the bubble shape and the parameter list says 'Pixshape=Pixel/Circle'. ===================== HOP - Fractals in Motion ================= Page 73 8. Press ctrl-backspace (undo all). This will undo all the changes you made and restore the original look from the demo file. 9. Let's get rid of all those special effects for a moment. To reduce the bubbles to simple dot-pixels, we have to switch off several pixel properties and graphical effects one by one : Press ctrl-q to switch off those little white reflections, alt-q to switch off the black outline, shift-O to switch off the shadow effect, and alt-i to reduce the bubble-shaped pixels to simple dots. Alt-i erases the current image and the fractal is redrawn. Notice that with less special effects on, the fractal grows a lot faster. If you prefer pure math over all the fancy effects, here's your 'classical' design. 10. Save the current fractal to a parameter file. To do this, press s. The image will be replaced by the Read Page of the user interface. The top line on the screen informs you that HOP is currently playing parameter set DEMO. You can save to 1. Image Parameters, 2. a GIF image, or 3. a color map file. Highlight the first option and press Enter. This will stop DEMO from playing and close the file. A filename menu opens up and show the names of all *.HOP parameter files in your directory. Choose (new). The cursor highlights 'Classic Hopalong' which is the current filename. Press the 'cursor up' key and replace HOP0000 (which is default for a new parameter filename) by TUTORIAL. Press Enter to save the current parameter set. The bottom line informs you that the save operation was successful. Press Enter. You will be returned to the image. 11. The 'classic' formula uses two constants (b=38 and c=66) which are displayed if the 'Show Values' screen is on. What happens if the constants have different values ? Press the * key on your keyboard. Every time, the constants will be set to random values and the fractal will be redrawn based on the new constants. The * key is nice to browse through different looks of the fractal. You can set the constants manually of course (this must be done from the user interface). 12. Press ctrl-backspace. The image will be redrawn with the original values. ===================== HOP - Fractals in Motion ================= Page 74 13. The variables list contains an entry for 'formula' (saying 'Classic' at the moment). Change the formula by pressing (small) f until the formula is Lattice1. The 'Lattice1' formula is very similar to 'Classic' but it tends to produce systems of connected circles. The three initial circles will soon be surrounded by more circles. 14. Press the Pos1 key to restart the image, then press (small) l to switch on the 'Connect' feature which connects consecutive pixels by lines. Watch the resulting movement which tells us something about the fractal's internal structure and growth. 15. Press the n key twice. The variables list (under section 'Math Effects') now contains the entry 'everynth=3'. This means that not each pixel is displayed but only 1 out of 3. The connecting lines turn into revolving squares. 16. Press ctrl-backspace again. The image will be redrawn with the original 'Classic Hopalong' values. 17. Press ctrl-t. This will switch on a math 'special effect' called Transform. The variables list now shows a value (19.3) for the Transform factor, and the fractal is redrawn with a completely new shape. Press ctrl-t again: the original fractal without Transform is back. Press ctrl-t again: the transformed fractal is redrawn. 18. Starting out from the 'classic' formula and the original values for the constants b and c, we can get a series of different shapes by varying the Transform factor. Press alt-t several times to set the Transform factor to random values. The resulting shapes may not seem to have much in common, but they are in fact connected by the transform factor. Press alt-t until you get a nice shape, then continue by pressing t. The Transform factor will be incremented by a small value if you press t (watch the value on the variables list), and the resulting fractal will be very similar but not identical to the one you had before. We see that by incrementing or decrementing (shift-T) the Transform factor, we get something like snapshots or slices through a three- dimensional fractal. Keep pressing the t key fast (1 per 2 seconds). What you get is almost an animation! 19. Press ctrl-backspace again. The image will be redrawn with the original 'Classic Hopalong' values. Press ctrl-t to set the Transform factor to 19.3 again. ===================== HOP - Fractals in Motion ================= Page 75 20. You don't have to press t many times to get an animation. Based on the principle of incrementing/decrementing t, HOP contains an animation feature that has many facets. Press alt-f2 to set an animation preset called 'Fast Changes'. Starting out from 19.3, the Transform factor is quickly incremented (for this example, in steps of 0.022 which is represented as an Animation Speed of 22). For each consecutive value of this factor (= for each 'frame' of the animation), 44 pixels are drawn (Pixels/Frame). At the same time, the previous frame's pixels are erased. There is a variable called 'Del Queue' on the variables list showing the length of what is otherwise called 'Erase Queue' or 'Wipe Queue'. At the moment, the queue length is 2340 pixels - this is the amount of pixels visible at a given moment. The result is a quick and dirty flight through the different transformed shapes that are possible for the 'Classic' formula with these particular values for b and c. If you watch the variables change while the animation runs, you will notice that the animation is circular - it returns to a shape similar to what it had with Transform factor = 19.3 when it reaches a value of about 25. the < key to reverse the direction of the animation (the Transform value will be decremented). 21. Undo all changes by pressing ctrl-backspace, then hit alt-f1 to see a different animation preset (Slow Changes) with a higher value for Pixels/Frame. Slow Changes produces a very minimalistic succession of more detailed images, but the principle is the same. Watch the animation variables Transform, Pix/Frame, Speed, and Del Queue to see the difference between Fast and Slow Changes. 22. Hit alt-f3 to see the 'Lines' animation preset and the connected variables. Do the same with alt-f4 ('Dancing Beads') and alt-f5 (Kaleidoscope). All of these are variations on one theme: the inc/decrement of the Transform factor at a certain speed, with different settings for the Erase Queue and certain graphic effects (Pixel Shape, Connect, Symmetry). ===================== HOP - Fractals in Motion ================= Page 76 23. The animation presets are like 'factory presets' of a digital synthesizer, allowing quick access to a certain type of animation, but all variables can also be modified manually ! Press ctrl-backspace to undo all changes, then alt-f2 to set the 'Fast Changes' preset. Pressing Enter will get you to the user interface. Use the mouse to click on the 'Math Effects' navigation button, or press PgDn or PgUp until you get to the 'Math Effects' page. Modify the values that belong to the animation, then press Enter (or click on the 'Ok' button) to redraw. Repeat this until you get the idea. 24. Ok, enough of this ! Return to the image and press the space bar, press v to switch the 'Show Values' screen OFF, then lean back and watch HOP improvise on its own. If you see a real nice image evolving, modify it until you really like it, then save it to a file. ┌────────────────────────────────────────────────────────────────────────┐ │ APPENDIX E: WISH LIST │ └────────────────────────────────────────────────────────────────────────┘ I was unable to find a color mapping method that is sensitive to the shape (the different and distinct 'parts') of the Hopalong fractal. If anyone can think of an algorithm please let me know. Ideas for HOP are always very welcome, and if there is enough interest there will be a next version of HOP to which you can contribute. Michael Peters [Compuserve: 100041,247] August 1994 [Internet: mpeters@ibm.net] Have fun and a colorful day ! And ... Don't leave your wife, don't quit your job if you can't stop playing with HOP ! ===================== HOP - Fractals in Motion ================= Page 77 ┌────────────────────────────────────────────────────────────────────────┐ │ INDEX │ └────────────────────────────────────────────────────────────────────────┘ adjust color freq 45, 57 algorithm 69 animation forward 23 animation programs 48 animation speed 22 animation type 22 animation type 40 autoGIFsave 47, 48 average # of pixels 38 background 24 backspace 42 barcodes grid 31 beep 42 Berry, Bob 63 black&white pattern 24 .BMP 57 border 29 BPASCAL 64 brush (pixshape) 28 bugs 56 circle (pixel shape) 27 color divide 35 color frequency 33 color mapping 34 color pattern 25 color shading 37 colorscroll 32, 34, 43 colorscroll delay 35 colorsquares(pixshape)28 command 54 comment 47 comment (pixshape) 28 commercial use 58 company registration 58 CompuServe 61 conditional lines 30 configuration 41 connect 30 connett 25 connett circle 27 connett circle fill 29 Connett, John E. 26 constants 17 constants 18 continuous 33 coprocessor 3, 5, 38, 57 copyright 60, 61 Cramer, Andy 10, 58, 62 Crockett, Rob 63 ===================== HOP - Fractals in Motion ================= Page 78 dancing beads 30, 40 Day, Michael 63 delay 43, 43 density 38 Dewdney, A.K. 14, 26, 62 DOS 9 dotted lines 30 DTA 48 EGA 3, 32, 56, 57 ellipse 24 elliptic 27, 28 EMS 42, 43 erase oldest pixels 20, 22, 34 error 56 ERRORS.HOP 56 everynth 20 EXTERNAL.SSM 9 eyes 23 fadeout 42 flakes (pixshape) 27 .FLI 48 flicker 42, 56 formula 17 FRAC'Cetera 63 fractal name 44, 46 Fractint 25, 32, 44, 46, 62 Fractint MAP 33 FRUG 63 fuzzy (pixshape) 28 generate anim.parms 48, 54 .GIF 24, 43, 44, 57, 61 Graphdev 32, 62 grid 31 Haeckel, Ernst 14 Hanisch, Siegfried 9 Hargrave, Jordan 63 help 16 hexagon grid 31 HOP directory 9 HOP.EXE 9 HOP.INI 9, 41, 45, 64 Hopalong 14 HOPRUNS.TMP 11 HOPSAVER.BAT 9, 11 HOPSVR.HOP 9, 46 HOPSVR.PIF 4, 5, 10 HOPSVR.SCR 4, 5, 11 HOPTSR.EXE 9, 10 HOPZIP.EXE 5 horizontal lines 25 Horner, Jon 63 hotkey 15, 53 ===================== HOP - Fractals in Motion ================= Page 79 image save/restore 42 installation 5 Internet mailing list 61 irregular 33 kaleidoscope 30, 40 keep 42, 53 Kirsch, Dave 63 Koch, Olaf 9 line style 30 linear color mapping 34 lines (pixshape) 27 Lines animation 40 Mandelbrot 14 .MAP 32, 33, 43, 46 .MAP filename 33 Martin, Barry 14, 62 Mason, Dave 48 mailing list for HOP 62 maximum # of pixels 17, 42 minimalism 39 multiple image 24 Mulvey, Bret 25, 62 Murdoch, D.J. 63 noerase lines 30 Norton style mouse 42 or-combination 25 OS/2 3, 9, 56 OS2USER 9 oscillation 29 overlaid image 47 palette 37 palette editor 36 palette mode 33, 40 .PAR 44 parameter 46 parameter file 44 parameter set 66 Pascal 66 password 11, 54 pattern 18 .PCX 57 periodic 33 Peters, Michael 58 pixel fill 27, 29 pixel oscillate 29 pixel shape 27 pixel size 29 pixels per frame 22 plankton 18 ===================== HOP - Fractals in Motion ================= Page 80 plasma 24, 25 plasma granularity 26 plasma overlay 26, 35 position 17, 18 precomputing 43 PREVIOUS.HOP 42 print 57 pulsate 35 radial color mapping 34 random 25 random grid 31 randomplay 54 recenter 18 rectangles 27 reflection 27, 29 registration 54, 58 repeat 45 rerun GIF 45 resize 18 resolution 6, 41 retrace 42, 56 rings 25 rotate 21 rotate animation 23 rotation speed 23 save previous 42 Scientific American 14, 26, 63 Scott, Randy 58, 64 screensaver 9, 46 shadow 31 shareware 58, 60 show values 15, 41 Sierpinski 25 size 17 slideshow 43, 54 slow 39 spirals 23 sprite 36, 28 square pattern 25 squares grid 31 SSAVRS.ZIP 9 static colorscroll 35 Stone Soup Group 63 SuperVGA 3 support 61 SWREG 59 symmetry 29 ===================== HOP - Fractals in Motion ================= Page 81 TeamB 64 text mode 15 thick lines 30 tied colors 34 title display 45, 43 transform 21 transform animation 22 transform factor 22 triangles (pixshape) 27 tryangles (pixshape) 27 tuning 38 Tuning 66 tutorial 66 twinkle 31 unregister 54, 59 unstable fractal 17 user interface 15 user name 43 vertical lines 25 VESA 6, 41, 57 VGA 32, 57 video 6 video mode 6, 41 video test 41 vortex color mapping 34 Walker, Simon 64 warp 23 Wegner, Timothy 25, 62 Wenzel, Sean 63 wheel 25 Windows 3-5, 7, 11 World Wide Web 62 XMS 42, 43 xor-combination 25 Young, La Monte 39 Zazeela, Marian 39 zoom 19