17 Bit Software 1: Collection A

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PURPOSE This document introduces you to MandelVroom, outlines it's features, and tells you how to use it. READINGS For a good explanation of Mandlebrot calculations, I recommend you look up the Computer Recreations column in the August 1985 edition of Scientific American magazine. You may want to read a book written by Dr. Benoit Mandelbrot, called "The Fractal Geometry of Nature", published by W. H. Freeman and Company. Dr. Heinz-Otto Peitgen and Dr. Peter Richter have written a very nice book called "The Beauty of Fractals". It is published by Springer-Verlag. It has a some very nice pictures and is a good navigational guide. I recomend it. INTRODUCTION This program lets you navigate around the complex plane generating Mandelbrot pictures. Picture data is saved in RAM allowing you to quickly recolor pictures using a powerful coloration mechanism. Once you've generated and recolored a picture, you can save it on disk in one of two formats: ILBM and MAND. ILBM files are in IFF format. MAND files contain everything needed to recreate the picture. It can take a long time to calculate Mandelbrot pictures. MAND files allow you to save this precious data on disk. MandleVroom also has these features: - Assembly language 32 bit fixed point Mandlebrot picture generator - Assembly language Fast Floating Point Mandlebrot picture generator - Picture presets - Color palette - Contour palette - Mouse and graphics oriented user interface - High resolution, interlace and halfbrite graphics modes supported - Configurable number of bit planes - Source in public domain TERMINOLOGY You need to know the following concepts to use this program: - Generators and Generation - Navigation and Zooming - Aspect Ratios - Contours and Altitudes - Pens and Colors GENERATORS AND GENERATION The generators perform Mandelbrot calculations over regions of the complex plane. The generators produce a two dimesional array of iteration counts. MandelVroom treats these iteration counts as altitudes. You can use this program to navigate around the complex plane choosing regions to generate pictures over. Using preset locations as starting points, you can generate pictures. Once generated, you select a region within the picture that you want as the next picture. When you start the generator, you 'zoom into' the new location in the complex plane. ASPECT RATIOS An aspect ratio is the ratio between the width and height of a rectangle. A square is a rectangle with a one to one aspect ratio. The pixels on your screen have an aspect ratio that varies depending on graphics mode you are using. MandelVroom takes the aspect ratios of the pixels into account when calculating pictures. Some Mandelbrot programs allow you to strech either the X or the Y axis. In this case, a square picture window would not represent a square region in the complex plane. MandelVroom will not allow you to do this. CONTOURS AND ALTITUDES Map makers often use color to indicate altitude in when making contour maps. Contour maps usually have a 'key' indicating what colors relate to which altitude. MandelVroom treats iteration count as altitude. It has a programmable key allowing you to assign pen numbers to ranges of altitudes. MandlVroom's programmable key is called the Contour Palette. The Contour Palette contains thirty two contours. You can use the thirty two contours' heights and colors to control the distribution of colors in your picture. PENS AND COLORS MandelVroom supports low resolution, high resolution, non-interlace, interlace, and half brite graphics modes. In these graphics modes, the Amiga uses a hardware color indirection method for graphics display. The Amiga hardware contains thirty two pens that can be filled with one of 4096 colors. The following chart show how many pens the Amiga hardware supports for each graphics node. Graphics Mode Number of Pens ---------------- ----------------- High Resolution 16 Low Resolution 32 Half Brite 64 Please note that interlace does not affect the number of pens available to you. MandelVroom has a Color Palette that allows you to copy, blend and exchange colors in the Amiga's color registers. STARTING MANDELBROT This version of MandelVroom can only be run from the CLI. To start the program, type: MandelVroom When the program starts, it opens a custom screen and a Picture window. It then generates a picture of the main Mandelbrot set. It will take a minute or two it to calculate this picture. THE MAIN MANDELBROT SET The black region in the middle of the picture is the Mandelbrot set. The bright area surrounding the Mandelbrot set is the place to explore. The darker regions outside the bright areas are of little interest. They are dark so they don't distract you from the interesting areas. NAVIGATION The Mandelbrot set is inside a circle of radius two, ceneterd about the origin of the complex plane. The rectangular Picture window represents a rectangular region on the complex plane. The pictures that MandelVroom generates depend on the regions you pick in the complex plane. MandelVroom generates pictures in the Picture window. You can choose regions within the current picture to be the boundaries for the next picture. When you generate, you will produce a big picture of the new region. This is nicknamed 'zooming'. ZOOMING IN There are three steps to zooming in. 1. Select a region for the next picture 2. Resize the Picture window if you like 3. Generate a new picture You select a region of the current picture using the Zoom Box. The Zoom Box is a resizable and movable rectangle you use to box in a region for the next picture. THE ZOOM BOX You place, move, resize and close the Zoom Box using the mouse. The following steps will open the Zoom Box in the Picture window: 1. Pull down the Zoom Box item's Open sub-item 2. Place the mouse cursor in your Mandelbrot picture. 3. Depress and hold the left mouse button 4. Drag the mouse down and to the right 5. Release the left mouse button. The Zoom Box is a stick figure of an Intuition window. The Zoom Box has a drag bar, resize gadget, and a close gadget. The drag bar and close gadgets are at the top of the Zoom Box. The resize gadget is in the lower right hand corner of the Zoom Box. The Zoom Box looks like this: +--- Close Gadget +--- Drag Bar | | v v +-----+----------------------------------+ | | | | | | +-----+----------------------------------+ | | | | | | | | | | | | | | | +---+ | | |<---- Resize Gadget | | | +------------------------------------+---+ This is how you move the Zoom Box: 1. Place the mouse cursor in the Zoom Box's drag bar 2. Depress and hold the left mouse button 3. Drag the Zoom Box around with the mouse 4. Release the left mouse button This is how you resize the Zoom Box: 1. Place the mouse cursor in the Zoom Box's resize gadget. 2. Depress and hold the left mouse button 3. Resize the Zoom Box using the mouse 4. Release the left mouse button You can close the Zoom Box one of two ways: 1. Press the Zoom Box's close gadget 2. Pull down the Close subitem of the Zoom Box item If you place a Zoom Box, and then decide you don't want to zoom, you can close the Zoom Box. RESIZING THE PICTURE WINDOW Once you've placed and sized your Zoom Box, you will want to resize the Picture window to have the same aspect ratio as your Zoom Box. If you don't, when you generate you may get too little or too much of the area on the right side of the Zoom Box. GENERATING NEW PICTURES If you pull down the Generate item of the Project menu, MandelVroom will generate a new picture for you. Using the zoom box and the generator, you can repeatedly zoom in until you find things you think are interesting. STOPING THE GENERATORS Pictures take from minutes to hours to generate. You can stop the generator by pulling down the Stop item of the Project menu. Once stopped, the generators can not be restarted, except at the begining of the picture. Once the generator is stopped, you can proceed as though the whole picture was calculated. CHANGING MAGNIFICATIONS MandelVroom is like a microscope with variable magnification. Every time you zoom in and generate a new picture, you increase the magnification of your microscope. You can also change the magnification by changing the height of the picture window. Making the picture window taller increases the magnification. Making the picture window shorter decreases the magnification. If you make the picture window wider, while not changing it's height, you will not change magnification factor. You will get a picture covers a wider piece of the complex plane. If you want to make a large version of a small picture, all you need to do is resize the window and generate. You must take care to make sure the aspect ratio of the original window and the new window are the same. If you make the picture too narrow, some of the things you want in the picture may be cut off. If it is too wide, you may have extra things in your picture. The same is true for the relative aspect ratios of the zoom box and the picture window. GOOD NAVIGATING This program has nice facilities for zooming into the Mandelbrot set. It is severly lacking in methods for zooming out. It's saving grace is that you can save interesting pictures to disk. You can also reload these pictures and resume zooming. You can use use disk files to record your journey in search of the ultimate Mandelbrot picture. File access is discussed in the LOADING AND SAVING section. The best way to be a good navigator is to practice. Start by generating a picture of the main Mandelbrot set. Zoom in on the perimiter of the set. Try not to get too much Mandelbrot in the picture, it takes a long time to calculate. If you like the picture, you can save it on disk, and zoom somewhere into the picture. Keep doing this and you are bound to find something nice. Good navigating is an art. Good subject placement and framing can make a world of difference in a picture. Sometimes you want lot's of detailed real estate in the picture (like a picture of Yosemite Valley.) Other times you want to isolate and capture a small object (like a picture of a small flower.) WHAT'S NEXT Once you have a picture generated, you probably want to recolor it. The next section explains how to pick and choose colors for your picture. PICTURE RECOLORING You can use the Color Palette and the Contour Palette to recolor a MandelVroom picture. You can use the Color Palette to affect the colors in you pens. You can also use the Contour palette to change the distribution of pens and colors in your picture. The next section explains the use of the Color Palette. The Contour palette is discussed in the THE CONTOUR PALETTE section. THE COLOR PALETTE You can open the Color palette by pulling down the Color item of the Edit menu. The color palette looks like this: +---+-------------------------+---+---+ | . | Color | | | +---+-------------------------+---+---+ | | | ++ ++ ++ ++ R G B +---+ | | ++ ++ ++ ++ | | Copy | <-- copy a pen's color | ++ +---+ | | ++ ++ ++ ++ | | ++ ++ ++ ++ ++ +---+ | | | | Spread | <-- Spread from pen to pen | ++ ++ ++ ++ +---+ | | ++ ++ ++ ++ ++ | | +---+ | | ++ ++ ++ ++ | | Exchg | <-- Exchange two pens | ++ ++ ++ ++ +---+ | | | | ++ ++ ++ ++ | | ++ ++ ++ ++ | | | | ++ ++ ++ ++ | | ++ ++ ++ ++ | | | | ++ ++ ++ ++ | | ++ ++ ++ ++ | | | | ++ ++ ++ ++ | | ++ ++ ++ ++ | | | +-------------------------------------+ ^ ^ ^ ^ ^ | | | | | | | +--+--+-- RED/GREEN/BLUE potentiomenters | | +--------+- Pens ADJUSTING PEN COLORS You can use the Red, Green, and Blue potentiometer gadgets to adjust a pen's color components. The following steps show you how to change a pen's color: 1. Click the mouse on the pen you want to modify. 2. Adjust it's color using the R/G/B potentiometer gadgets. COPYING PEN COLORS You can copy one pen's color into another pen by performing the following steps: 1. Click the mouse on the pen you want to copy 2. Click the Copy gadget 3. Click the pen you want to change SPREADING PEN COLORS You can create a range of colors between pens (e.g. a range of pens from dark green to light green) using the Spread gadget. You use the spread gadget in the following way: 1. Click the mouse on a pen at one end of the range 2. Click the Spread gadget 3. Click the mouse on the pen at the other end of the range EXCHANGING PEN COLORS These steps will exchange two pen colors: 1. Click the mouse on one of the pens you want to exhange 2. Click the mouse on the Excg gadget 3. Click the mouse on the other pen NOTES ON CHANGING PEN COLORS Be very careful when changing the top four pens in the left most column of pens. These pens are used by the system to render windows and screens. If you make these pens the same color, you may have problems seeing MandelVroom's controls. The Amiga uses pens 17 through 19 when drawing the mouse cursor. If change these pens, the cursor may be hard to work with. The Zoom Box on the picture window is rendered using a drawing mode called complement. When the system is drawing a line in complement mode, it negates the pen number in each pixel in the line. If you have five bit planes, you have thirty two pens. The complement of pen 0 is pen 31. It you draw a line in complement mode, you can erase it by drawing the same line again in complement mode. If complementary pens have similar colors in them, then object drawn in complement mode is unnoticable. If you have problems finding your Zoom Box, check out your pen colors. THE CONTOUR PALETTE The Contour Palette is a powerful control mechanism for coloring your Mandelbrot pictures. It has thirty two contours. Each contour has a pen and a height. MandelVroom expects to find the contours' heights decreasing as you traverse the list of contours from 0 to 31. Given this, a contour actualy represents a range of heights. Here is an example description of the list of four contours: Contour Contour Contour Contour Number Height Pen Range ------- ------- ------- --------- 0 1023 0 1023-1023 1 500 10 1022-500 2 300 1 499-300 3 100 2 299-100 OPENING THE CONTOUR PALETTE You can open the Contour palette by pulling down the Contour item of the Edit menu. The Contour Palette looks like this: +---+-------------------------------------------+--+--+ status line -> | | C: 0 H: 1023 P: 0 | | | +---+-------------------------------------------+--+--+ | | set pen or --> | .. .. .. .. .. .. .. .. .. .. Set +---+ | height gadgets | .. .. .. .. .. .. .. .. .. .. .. | | ReColor| | +---+ | increment --> | .. .. .. .. .. .. .. .. .. .. + | height | .. .. .. .. .. .. .. .. .. .. | | +---+ | +-> | .. | | Smooth | | | .. +---+ | | | | | | .. | | | .. | height | | Alt. | potentiomenters | .. | | | .. | | | | | | .. .. .. .. .. .. .. | +-> | .. .. .. .. .. .. .. | | | | | decrement --> | .. .. .. .. .. .. .. .. .. .. - | height | .. .. .. .. .. .. .. .. .. .. | | | +-----------------------------------------------------+ ^ ^ ^ ^ | | | | +---------- Contours ---------+ | + Commands 0 1 2 ......... 30 31 | +-- Ceiling As the generator calculates pictures, it saves the data in RAM. Once the picture is generated, you can change the Contour Palette and recolor the picture. When you push the 'ReColor' gadget, MandelVroom traverses the Mandelbrot data, converting altitude to pen, and plotting pens in the picture window. This mechanism allows you to recolor the picture quickly and repeatedly until you are happy with the way it looks. Each contour has four gadgets: a set gadget, an increment height gadget, a height potentiometer, and a decrement height gadget. ÿÿüÿÿüÿÿüÿÿøÿÿðÿÿàÿüüÿÿÿàÿÿðð`@ÿÿøÀÿÿüÃãðÿÿüð`Àÿÿü`ðÿÿøóð`ÿÿðÿÿàÿü