
                                                               Welcome to 
                                      EasyFractal 
                                  Programmed with Omikron Basic
                                  and the EasyGem Library

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Overview:

      - General Info
      - 10 Minute Quick Start Tutorial ...
      - EasyFractal Menus
      - Fractal Editor
      - Palette Editor


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                                                                 General

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System Requirements

EasyFractal 3 runs on Apple computers with Power PC processor and System 8.6 or higher. However, it is recommended using at least System 9 because so-called floating windows are not supported by the operating system in previous versions and EasyFractal makes extensive use of this property. The available memory should amount to 16 MB.
EasyFractal 3 is a so-called Carbon Application. If Mac OS X is installed on your computer, the program is automatically launched under this operating system. If System X is not installed, the program also starts under Mac OS 8.6 or 9.xx. However, in this case CarbonLib has to be installed in version 1.2 or later. This is usually always the case unless you actually deleted CarbonLib or suppressed its installation when setting up the operating system. 
The program does run in 256 color mode without any problems, but it is recommended to select a higher pixel depth (thousands or millions of colors), since the fine color progressions are then much more effective.


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Installation

If you obtained EasyFractal as a compressed file (e.g., from the Internet), all you have to do is unpack the file and indicate to the unpacking or unzipping utility where to place the EasyFractal folder (on the hard disk). If your version of EasyFractal is not compressed (e.g., on CD), just copy the EasyFractal folder to a suitable location on your hard disk. 
The installation does not create any hidden files so that you can easily uninstall EasyFractal by dragging its folder to the trash icon.


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Unregistered Version Restrictions

The following restrictions apply to the unregistered version:

1. A dialog box opens every 10 minutes informing you of the unregistered status of your program.

2. PICT format images can be saved only with a resolution of up to 800 x 600 pixels.

3. Images can be printed only with a resolution of up to 800 x 600 pixels.

4. Maximal 5 fractal windows may be open at the same time.

5. Images created with the unregistered version may not be used commercially.


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Starting EasyFractal 

Start EasyFractal by double-clicking on the program icon. EasyFractal starts very quickly and immediately opens four windows. 
The traditional Mandelbrot's Fractal is displayed in the upper left corner, as most everybody interested in fractals has probably already seen. A text window displaying these instructions is located slightly off to one side. 
The upper right corner features the Palette Editor and the Fractal Editor is below that. Memorize these terms because we will continue to refer to them during the course of these instructions. The last two windows are so-called floating windows. Floating windows are always displayed on top of all the other windows. They are therefore perfectly suited to display editing tools.

Caution: The float property is not supported until Mac OS 9. Older operating systems display the floating windows as normal document windows.

if you are still working with an unregistered version, a dialog box prompting you to register will also appear every 10 minutes. 


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General Info about Fractals

We as humans continuously attempt to use our technology to describe the world with simple geometric objects (lines, squares, circles, etc.), while Mother Nature chooses a different path to build complex structures. Nature uses the principle of self-organization and the associated self-similarity. For example, if you look at a tree and then saw off a branch, this branch with its sub-branches is similar to the entire tree. 
This principle of self-similarity is the fundamental construction principle of nature surrounding us. Typical examples are the already mentioned tree, but also other plants such as broccoli, the capillary system of humans and animals, desert landscapes where bigger dunes consist of smaller dunes, coast lines, etc. The list is endless and one is hard pressed to find anything in nature that is not subject to this principle. 
The fascinating aspect is that these extraordinary structures are generated from very simple rules simply by repeating them a billion times over. This sounds like a job for a computer because computers are well-known for not being especially intelligent but able to repeat repetitious tasks over and over at incredible speeds, e.g., preprogrammed tasks formulated as simple algorithms. 

And that leads us to EasyFractal because these self-similar, complex structures are also known as fractals. Special forms of these fractals are Mandelbrot and Julia sets, named after their discoverers. By selecting suitable parameters and colors, very pretty and extremely aesthetically pleasing images can be generated and that is where EasyFractal comes into play. You can modify a vast number of parameters and thus generate a virtually endless number of images. 
Due to the enormous time it takes to manually calculate a fractal, computers come in very handy, but even the very fast processors of modern computers require a programming language that generates highly optimized programming code. EasyFractal was therefore programmed with Omikron Basic in its entirety, while the user interface was generated with the EasyGem Library.


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First Steps Using EasyFractal

Once the program starts, one window is already open, displaying the well-known Mandelbrot's Fractal. This picture is NOT stored somewhere but instead is being calculated in real time. This means it is possible to scroll around the virtual screen as desired by clicking on the control elements of the window or using the cursor keys.
The increment of each step can be set with the number keys 0 to 9. The increment of each step is calculated using the formula "Increment = 2^ Key." For example, if you push 3, the increment is 2^3=8.
The info line shows the current mouse position; however, not in pixels as usually but as REAL and IMAG portion of a complex number (Z=Zr+i*Zi), since the calculation of Mandelbrot and Julia sets is carried out within the complex number plane. 

If you have a special interest in an area, (e.g., at the edge of the "Apple Figure"), just keep the ALT key depressed while clicking with your mouse on the point that you would like to explore further. This point will then move to the center of the window and the zoom will enlarge the picture at that point. This process will be repeated as long as the mouse button is pressed. 
Zooming into a picture you will notice that the image is not blurry. The reason for this is that the enlarged images are recalculated each and every time you use the zoom function and without restricting the resolution as it is the case when zooming into a normal pixel image. 
Yet, there is a drop of bitterness: The calculation accuracy of the processor (approx. up to 15 or 16 decimal places) is not sufficient when zooming about 10 billion percent to distinguish between points that are close together. Individual pixels then become small squares. 
Of course, you can also zoom out again. To zoom out select the CTRL key instead of the ALT key or use the Undo function.

The individual functions of EasyFractal are discussed in detail in the other chapters and a brief tutorial will give you a first glimpse of the possibilities of this program. Access the other chapters by using the popup menu in the upper right corner of this window.
If you would like to print out this manual, we recommend setting the print size to 80% in the Page Setup ... menu item of the File menu because then the text will fit exactly on a normal page.
We hope you will enjoy this little program and recommend visiting the Omikron Basic Homepage on the Internet if you would like to program such items yourself. The Omikron Basic Homepage features the EasyFractal 1.01 source code you can use and modify yourself, e.g., to add new iteration functions. 


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EasyFractal News on the Internet:
                http://www.berkhan.com

or contact:
             Berkhan-Software
             Alt-Isenhagen 19
                D-29386 Hankensbuettel
                Germany
                Phone: +49 5832/979895, Fax: +49 5832/6160
                Email: info@berkhan.de

