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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...

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In 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,...

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Monday 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...

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Quaternion Travels

Relax to a slow flythrough of an interesting neighborhood of the quaternion Julia sets.

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Our 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...

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River 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...

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Lorenz 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...

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Color 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...

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Convergence 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...

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The 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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