Feigenbaum, by David Martinez
Mitchell Feigenbaum discovered two basic constants governing all processes that period-double or bifurcate to chaos. Many natural events unfold to rhythms of these two numbers. One example is the transition when the stream of water from a pipe goes from a steady flow to chaotic dripping. The disintegration of the wake behind a ship into chaotic eddies is an other example. The fractal diagram of this phenomena is called the Feigenbaum Fractal Tree. The first number, 4.66920... , is the ratio between the length of successive branches, and the second number, 2.50290..., is the ratio of their diameters.
Feigenbaum’s name happens to mean “fig-tree” in German. I have him shaking a golden fig tree near his lab at Los Alamos, New Mexico, where he was working when he made his discoveries. The butterflies, the rocks, the mountains, and more period-double. I have hidden Feigenbaum’s numbers among the foreground flowers like a color vision test.
David B. Martinez © 2011
