Anthony Mattox Interaction Design + Digital Art

I created this Context Free Art script a few months ago and revisited it to tweak it a bit and make some nice high resolution renderings. This is a great illustration of what I find so fascinating about fractals. Computers are often considered the antithesis of organic growth, however, their incredible ability to replicate such processes seems to be in the very nature of object oriented programming. The complexity that can be formed from such simple rules and patterns continues to amaze me.

Although a mathematics purist may not willingly call this a fractal, it is in my opinion a prime example. I think Benoît Mandelbrot would agree with me. It is a mathematical function which, through a simple iterate system, fantastically mimics physical structures. It also has the properties of self similarity over infinite scale which is indicative of fractals.

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If you are interested in geometric fractals, Context Free Art is a very interesting program it play with. The interface consists of a code area on the right, and a rendering area on the left. The very simple script only contains a few commands, but through recursion can create fantastic fractals.

The script allows you to draw squares, triangles, and circles, and to transform them in a few different ways and color them. You can create custom rules which transform whichever rule they contain. By creating recursive functions like this just about any geometric fractal can be created. Although the program is very limited, I find it very interesting how much can be created only with transformations of three basic shapes. The program also has the ability to export both raster (pixel based) and vector images, which makes it a useful tool for creating shapes and textures, and renders the script live. If you would like to go further with fractal generation, I recommend Processing, but Context Free Art is so simple to learn it’s a fun tool to play around with.

Simple recursive functions can created complex geometric fractals. A function draws a graphic and then by calling itself any number of times creates branches in the image. Each of the branches follows the same algorithm and creates the fractal. The transformations which occur between iterations, the graphic drawn, and any other steps or even randomized algorithms within the process determine the resulting fractals structure. This video of a fractal programmed in Processing is one of the simplest geometric fractals. Each iteration produces two copies of itself at it’s end. More complex versions of such a function are used to generate trees and other structures in video games and other virtual environments. The rotations of these two branches are changed slightly each frame and the function is recalculated. Within an object oriented programming language like Processing, each iteration could also create a new object or pass values into an array allowing the data to be easily reused without re-running the entire function.