There are two methods for producing fractal geometry. The first method, the decomposition, is the most easily understood. In a decomposition we apply an algorithm that breaks up the geometry of some starting point into several parts. We then re-apply this algorithm to the smaller parts created, obtain many more, even smaller parts, and continue this reiteration until we have reached the complexity limit at the smallest scale of object we can possibly make. This is how an architectural design proceeds because it reflects the way that building proceeds.

From time to time I happen upon an attempt to "do" complexity that completely misses the point. In this first installment of many "Fake Complexity" topics, the culprit is Rem Koolhaas and his CCTV Headquarters for Beijing.

The immensely productive Physicist-Mathematician-Entrepreneur Stephen Wolfram theorized, based on his studies of cellular automatons in the 1980's, that there exists four classes of physical processes in the universe. Class I is simple continuous behavior (line). Class II is repetitive behavior (checkerboard). Class III is nested, hierarchical-fractal behavior (basic fractals like the Sierpinski triangle). Class IV, the most fascinating, is chaotic behavior (random fractals such as the Mandelbrot Set).