What are Fractals?
Fractals are figures and objects that are self-containing in recursive fashion. Fractals can be generated by recursive application of mathematical functions. Any part of the object is a replica of the whole object, but of a smaller size, to infinitesimal levels.
The world of fractals are very fascinating. The recursive nature of fractals and how close they resemble natural elements make it an important facet to mathematics and computer graphics. The advent of computers have helped in creating fractals that depict natural elements accurately.
String Systems
String systems have been used to depict fractals. There are many books that go into details of these mathematical representations of some fractals.
This representation consists of an axiom string, transformation rule strings and angle of turn. The axiom string is transformed recursively by applying the transformation rule strings to each character in the axiom string.
After expanding to a finite level (due to the restriction imposed by the detail that can be represented on a monitor and memory available), the string is interpreted as movements of the cursor over the screen. The different movements include turns, drawing forward and moving forward (without drawing on screen).
With this simple system any number of fractals can be created, by using different axiom strings, different transformation rule strings and angle of turn.
Example
The example of a Koch Curve, shown at the top of this page, is generated using repeated iterations. Axiom is "F", transformation rule for "F" is "F+F--F+F", angle of turn is 60 degrees and number of iterations is 5.
The iterations upto the maximum possible is repeated after a short duration. Since Netscape 4.0x does not recognize the java listeners well, the example above had to be changed in this manner.
See more sample fractals in any of the following pages.
Conifer bush
Sierpinski Triangle
Hexagonal Gosper
Plant for a pot
About the screen saver
This screen saver is a generalized string system based two dimension fractal generator. In this case, it has been created with many in-built axioms, along with appropriate transformation rule strings and angle of turn.
The user can choose from a particular category of fractals or choose to use all the fractals. The display can be in sequence that the rules are stored in, or in random order. The user can either choose to blank (black) the screen when the screen saver begins or draw the fractals over the existing image of the screen. The user can also choose to blank the screen before each fractal is drawn or to keep drawing more fractals over existing image. The user can also control the interval between one fractal display and next.
For each fractal the number of iterations has been pre-programmed due to either memory limitations or display resolution limitations. The categories have been named by me.
Download the free screen saver
The screen saver is provided free with no guarantee or warranty. See the License Agreement before you download. Unzip the downloaded file, copy into the WINDOWS directory and rename the file appropriately, preferably Fractal Dimension.scr. Then the screen saver should automatically appear in the list of screen savers, under Display option of Control panel. Please note that the name that appears on the dialog will be the name of the file.
If you are using Microsoft Internet Explorer, just click on the link below to download the screen saver. If you are using Netscape, then the link may bring a screen with junk, since it is an executable. You can still use "Save As" option of the browser and get the executable to your PC. I have not tested other browsers. Let me know if you have any problems and I can email the screen saver to you.
Download the screen saver for Windows 3.1, (also runs on Windows 95). This is version 1.0 released on the web on 15 March, 1998.
Download the screen saver for Windows 95 & Windows 98. This is version 1.1 released on the web on 15 March, 1998. We have received feedback that this version runs on Windows NT also.
Future Updates
The above versions are not animated. The whole fractal is drawn in a fraction of a second. In the near future, an animated version will be released. More customization options will also be included.
A release containing user's customization of new fractals using simple ".ini" text files (that will contain the axiom string, expansion rule strings and angle of turn) under Windows 95/ Windows 98 is also being contemplated.
Feedback
Your feedback is very valuable. Kindly email me your comments, criticisms, suggestions and questions.
Have fun.
Vasu
