Search: ex:EX4117
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| BP344 |
| Shape can tile itself vs. shape cannot tile itself. |
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COMMENTS
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Left examples are sometimes called "rep-tiles."
The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.
Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram." |
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CROSSREFS
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See BP532 for a version with fractals.
Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349
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EXAMPLE
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Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves. |
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KEYWORD
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hard, nice, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional
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CONCEPT
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recursion (info | search),
self-reference (info | search),
tiling (info | search),
imagined_shape (info | search),
imagined_entity (info | search)
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WORLD
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shape [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP820 |
| Shape can be combined with a copy of itself to form a convex shape vs. not so. |
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