Ξ 0.18
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The law of large numbers in action.

2400 x 2400 resolution.

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Clayton Shonkwiler

Hi Dannie,

There are 512 total paths starting at 512 equally-spaced points along the unit circle. Each path progresses steadily around the circle in the angular direction, but the amplitude (distance from the center of the circle) traverses a so-called Brownian bridge starting and ending at 1 (Brownian motion describes the motion of particles that are constantly being deflected by other particles; a Brownian bridge just means Brownian motion that is required to return to its starting point in a fixed time). This means that the expected location of each path is always exactly on the unit circle, which makes the collection of all paths form a sort of fuzzy circle.

Also, the color of each path is chosen based on its average distance from the center: paths which are on average closer to the center are darker than those that are on average further from the center.

This was coded in Mathematica; you can see the source code here:


This is really fascinating, can you share what function or procedure you used to generate this piece?


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Ξ 0.18