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Zeno Rogue

17 Apr, 3 tweets, 2 min read

A rainbow of birds is flying in a hyperbolic manifold. Each one flies in a straight line, and initially, they form a tight single file. However, because of numerical precision errors, they quickly end up flying all over the place. #mathart (1/3)

This is because of negative creature: when two birds fly "parallel" with a short distance between them, new space grows exponentially between them. The videos start 20s after the start of the simulation -- you need only this much time (in the current implementation). (2/3)

A three-dimesional version -- unfortunately it is more difficult to see what's going on here. (3/3)

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Zeno Rogue

@ZenoRogue

6 May 20

We have already see this: the space of rotations of the sphere. As well known in 3D graphics, this space is the same as unit quaternions, i.e., a 3-sphere (with opposite points identified). Today, we will modify this to get a new geometry! (1/6+)

The straight lines you see are called fibers. We change the geometry by stretching the metric along the fibers. As if the speed of light was slower/faster along the fiber, and light still took the fastest route, as usual.

Here we stretch the fibers to just 2%. There is only one white block on every fiber -- but since it is so fast to travel along the fiber, we see many copies of every white block! In the limit we get the S2xE geometry.

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