Well I

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Folding instructions: Well I
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This is the primary page for this model.
Paper: Tant
Type: classic tessellation, abstract aperiodic tessellation (implies: abstract tessellation, abstract, geometric, pattern, abstract periodic tessellation, non-recursive periodic tessellation, periodic tessellation, tessellation)
Author: Michał Kosmulski
Colors: red
In albums: Models with Dubious Classification, Pythagorean Tiling Family, Showcase, Tessellation Examples

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In this tessellation, rectangles are arranged in layers around a central square. I called it Well since it reminds me of a perspective view looking down a well lined with bricks. There are a few other similar arrangements, and I have seen some used as tiling patterns on floors. This work is from a 32×32 grid, but a 16×16 grid is enough to get a feeling for its structure.

This tessellation is a flagstone on both sides. The structure is closely related to Pythagorean Tiling and Brick Road with just the arrangement of twists around the rectangles and rectangle proportions differing.

In contrast to most of my designs, this tessellation is neither periodic nor recursive, even though it can go on indefinitely given a large enough grid. It seems, however, that one can also tile several such wells (of arbitrary size) side by side, so whether this tessellation is periodic or not will depend on whether you view the work seen here as a part of a single, infinitely large molecule, or a single finite molecule that can be tiled. Update: it can be tiled (and thus made periodic) indeed.

Depending on how you look at this pattern, you can either consider the bricks to be placed in concentric square “rings” of increasing diameter, or on a single spiral which winds around the center turn after turn.


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