Fractals
I’ve been interested in fractal geometry for a very long time, since I read an article in a magazine in the early ’90s describing how to generate the Mandelbrot set. Unfortunately, at that time, I didn’t know complex numbers which are required to generate the set. I came back to it many years later, when I learned more mathematics and programming. Fractals constantly amaze me how easily simple mathematical rules can create extremely complex structures imitating natural phenomena.
In the following sections, I have presented my studies and programs to generate fractals. Fractal images on my website were created with them. Most writings are in Polish only, but I invite you just to see the generated pictures and my animations of fractals.
Iterated Function Systems (2004)Iterative making of simple linear mappings can lead to really surprising results, leaves, trees and snowflakes. I wrote a program that allows to study such geometrical constructs, as well as affine mappings they are based on.
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Lindenmayer systems (2005)The plant development modelling language proposed by A. Lindenmeyer allows to create incredibly real natural objects, plants, trees and snowflakes. I wrote a Java applet that allows to experiment and browse through various L-Systems structures. This presents only a small part of what can be found in the book “The Algorithmic Beauty of Plants” by Lindenmeyer. | |
Other types of fractals (2004)In this section, I wrote a brief survey of other types of fractals. You can find here several further programs, descriptions and images of: the Newton fractals, Mandelbrot and Julia set, fractal flames and others. | |
Short animations with fractals (2006)I created several short animations with fractals in 3D Studio Max. Fractals presented in the animations include the Mandelbrot and Julia set, Sierpinski pyramid and carpet, Wada Basins, Cantor dust, the Menger sponge and others. |