Chaos Theory
Iterated Function System

The concepts of chaos theory are rather extensive and intricately complex.  This section attempts to provide a considerably simplified explanation of chaos theory for the purpose of understanding how it contributes to fractal design.  The concepts of dynamical systems, attractors, strange attractors, and the “butterfly effect” are covered, as well as a spotlight on Edward Lorenz, originator of many of the postulates integral to chaos theory.

go to "Chaos Theory"

This section explores the methods used by iterated function systems to create fractal shapes.  A quick introduction leads into detailed explanations of shape and point iterations, complete with visual references.  The spotlight in this section is dedicated to “Barnsley’s Fern”, a popular example of point iteration that also illustrates how fractals exist in the natural world.

go to "Iterated Function System"

Benoit Mandelbrot

The French-American mathematician, Benoit Mandelbrot, is noted for coining the term “fractal” that is used to describe both the phenomenon in chaos theory and its popular hybrid in art.  He believed that while fractals are based on chaotic principals, they are even more prevalent in life and nature than the shapes of contemporary geometry.  He is probably most well known among fractal designers as the creator of the “Mandelbrot set”, a complex fractal that forms an infinite depth of unique patterns along its edge.  A large (and ever growing) number of fractal designs in the art world of today began life as an intricate pattern found inside of an M-set. A more detailed explanation of the Mandelbrot set can be found in the Variations section.

Benoit Mandelbrot