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A color image of M.C. Escher's drawing "Circle Limit III." It is a map of the Lobachevsky upper half plane to a disk. The semi-circle geodesics are now arcs between points on the edge of the circle. A number of colored fish are drawn along these arcs; all the fish along an arc have the same color. They are longer near the center of the disk and shorter near its edge.

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A color image of M.C. Escher's drawing "Circle Limit III." It is a map of the Lobachevsky upper half plane to a disk. The semi-circle geodesics are now arcs between points on the edge of the circle. A number of colored fish are drawn along these arcs; all the fish along an arc have the same color. They are longer near the center of the disk and shorter near its edge.
https://files.mastodon.social/media_attachments/files/109/439/265/017/432/383/original/6c3f5d5a6b136dee.jpeg

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Robert McNees (mcnees@mastodon.social)'s status on Thursday, 01-Dec-2022 16:07:14 UTC Robert McNees
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You have probably seen this geometry before. It can be mapped onto a disk by a Möbius transformation, which preserves relationships between straight lines. The x-axis becomes the edge of the disk.
The geometry of this "Poincaré disk" inspired M.C. Escher's "Circle Limit" series of drawings. In this case the rulers are the fish-lengths. See how they get small as you approach the edge?
Image: M.C. Escher, "Circle Limit III"

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