Search: concept:self-reference
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| BP188 |
| Shape of whole different from shape of parts vs. shape of whole same as shape of parts. |
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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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| BP390 |
| Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms. |
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| BP529 |
| Fractal tiles itself with smaller non-rotated (nor reflected) copies of itself vs. fractal requires turning to tile itself. |
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| BP530 |
| Fractal tiles itself with uniformly scaled-down copies of itself vs. fractal tiles itself with stretched copies of itself. |
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| BP531 |
| Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself. |
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| BP532 |
| Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself. |
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| BP533 |
| Contains smaller copy of itself vs. doesn't. |
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