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Most visualizations of the Lorenz attractor are of a long history of a single point after convergence to the attractor has occurred. I was interested in what the surrounding space looked like, so I randomly selected 20,000 starting points from a three dimensional Gaussian distribution with a standard deviation of 100. Each point was iterated, [...]

Another visualisation of the Lorenz attractor discussed in Lorenz and the Butterfly Effect, color cycled between green and blue. A path of one million points, newer values are green, older values are blue. I’ve also produced some higher resolution stills with better antialiasing. Built with Processing.

In 1962, Edward Lorenz was studying a simplified model of convection flow in the atmosphere and discovered something that wasn’t simple at all.

A brain teaser goes as follows: a farmer is returning from market, where he has bought a wolf, a goat, and a cabbage. On his way home he must cross a river by boat, but the boat is only large enough to carry the farmer and one additional item. The farmer realizes he must shuttle [...]

Relax to a slow flythrough of an interesting subset of the quaternion Julia fractals.

This simulation of a school of fish allows you to play with the weightings of three rules that cause coordinated group behavior.

In the previous post, we discussed the Prisoner’s Dilemma and saw how a simple strategy called Tit-for-Tat enforced the Golden Rule and won a very interesting contest. But does Tit-for-Tat always come out on top? The most confounding thing about the strategy is that it can never win – at best, it can only tie [...]

Almost every decision we make involves someone else in one way or another, and we face a constant choice. Should we take advantage of them, go for the quick score and hope we never see them again – or should we settle for a more reasonable reward, co-operating in the hope that this peaceful relationship will continue long into the future?

Ski lift operators have proved that it’s not only conidae snails who can produce the Sierpinski triangle in their natural environment.

My three dimensional unfolding of the quaternion Julia sets finally finished rendering.