Fractal Programming

In honor of this year's Fractal Art contest I've decided to post about my experiences learning how to program fractals from one of Clifford Pickover's books on the subject.

I was initially struck how most fractals have a purely 2D output. In a sentence: you choose particular equation and chart the results of it on a real vs imaginary Cartesian plane and if you choose the right equations and limit said equations to the right values and you assign colors to right values, interesting pictures emerge. Yes, there is a lot of work involved, but the process is primarily about exploring mathematical equations. Fractal artists are more explorers than anything.

As I am most interested in 3D programming, Mandelbrot and Julia fractals are of less interest. However there are there types of fractals which are more useful, primarily because they work with objects rather than pixels. EDIT: I've recently discovered Quaternionic fractals, which create 3D fractals in Julia/Mandelbrot manner.

Branching
Interesting results emerge when you specify when and how a path or object should change its path or sprout new buds, tendrils, etc.











Tessellation Automata
TA requires that you define a grid (in 2 or 3 dimensions) and populate it with several objects (usually pixels). With each cycle of a program you determine if a pixel will give rise to offspring or die.










Packing
With packing you simply define an area and begin filling it randomly with objects so that every object must be as large as it possible can. As the space fills up, you the objects become smaller.

All of these work in 3D, and occur in nature.

Thu, Jan 3, 2008  Permanent link