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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.

I believe that ultimately human consciousness can be described by a program. Now this doesn’t mean we’re all in the Matrix, simply that our mind is a giant seething logical machine with values that are manipulated by rules.

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

In winter during the late afternoon before settling down to roost, flocks of thousands of starlings will twist and turn, turning the sky black with strange curves that seem to move with a mind of their own. The flocks of up to a million strong form for warmth, for security, and for social contact.

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?

A philosophy website recently conducted a very interesting survey about some of these greatest standing questions in philosophy.

When I was a kid, I used to wonder if everyone saw the world in the same way. We can all look at the same grass, but maybe the color I called green showed up in my brain as the color my friend called blue. Maybe all of our colors were shifted around to the [...]