Herds of Android Birds Mimic Ad Hoc Flocks
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...
View ArticleIn This Virtual Fish Tank, You Make the Rules
In my last post, I discussed how individuals following simple rules cause cause coordinated group behavior to arise. The boid model created by Craig Reynolds used three rules – alignment, separation,...
View ArticleMonday Miscellany
A few little things for Monday. I made a new video using the same engine as the fish school simulation described in the post In This Virtual Fish Tank, You Make the Rules. This video shows 5000 fish...
View ArticleQuaternion Travels
Relax to a slow flythrough of an interesting neighborhood of the quaternion Julia sets.
View ArticleOur Modular Minds
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...
View ArticleRiver Crossing Problems and Discrete State Spaces
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...
View ArticleLorenz and the Butterfly Effect
In 1962, Edward Lorenz was studying a simplified model of convection flow in the atmosphere. He imagined a closed chamber of air with a temperature difference between the bottom and the top, modeled...
View ArticleColor Cycled Lorenz Attractor
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...
View ArticleConvergence in the Lorenz Attractor
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...
View ArticleThe Theis Equation and Flow
Mathematics is remarkably effective in describing the physical world in part due to isomorphisms, relationships between concepts that reveal a similar underlying structure. In 1935 Charles Vernon Theis...
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