CLICK HERE for an excellent BBC program on YouTube that explains Chaos Theory wonderfully – highly recommended. (NOTE: VIDEO NO LONGER WORKS AS BBC TOOK IT OFF YOUTUBE – The program was called “The Secret Life of Chaos” so you can check it out elsewhere – it’s well worth it
In early high school my maths teacher was showing the class a film on geometry. The film showed squares and circles being drawn over shapes in nature such as flowers. Somewhat bemused I remember saying to the teacher “So what? – so what if you can draw a triangle over a flower – the flower doesn’t even look like a triangle or a pentagon.” To me it didn’t really make any sense. The film was all about Euclidean geometry and how we have used this knowledge to structure our material world. In the 1950’s a scientist named Benoit Mandelbrot wanted to find a mathematical basis for the rough irregular shapes of the world. He came up with the word fractal to explain a whole new geometry and discovered the Mandelbrot Set – some call it the thumbprint of God. Hooray – at last we have a geometry that actually looks like natural shapes and processes.
Many a year ago in the early nineties, a friend and I became engrossed in chaos theory. We started fooling about with a computer program called Chaos. One part of the program was an application called Cellular Automata. Basically this application ran an equation and colored cells (represented by computer screen pixels) according to the color of neighboring cells. To start the program a single cell was “seeded” and then the equation was let to run a number of times (iterations). Without going into boring detail we ran the program and then let it iterate all night and our result was obtained in the morning (computers in those days were very slow) and here at the top was our resultant image.
This may not look like much but to us at the time it was remarkable. By starting with such a simple mathematical equation or rule and then by applying feedback the end result is a complex picture that shows natural looking shapes. We were so excited because such spontaneous pattern formation was evidence of how potentially nature can create wonderful complexity out of incredible simplicity – it can self organize. Evidence of self organization can be seen everywhere you look – from shoals of fish, to traffic movements in a city, to cells differentiating in morphogenesis to the formation of sand dunes.
In the last few decades Chaos theory, fractals and all related goodies have captured humankind’s imagination and has inspired millions. It is my belief that the science of Chaos is only in its infancy and will begin to shape our lives more and more – Euclid eat your heart out bro.