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BP344 Shape can tile itself vs. shape cannot tile itself.
(edit; present; nest [left/right]; search; history)
COMMENTS

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."

CROSSREFS

See BP532 for a version with fractals.

Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343  *  BP345 BP346 BP347 BP348 BP349

EXAMPLE

Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.

KEYWORD

hard, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional

CONCEPT recursion (info | search),
self-reference (info | search),
tiling (info | search),
imagined_shape (info | search),
imagined_entity (info | search)

WORLD

shape [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP570 Shape outlines that aren't triangles vs. black shapes that aren't squares.
(edit; present; nest [left/right]; search; history)
COMMENTS

An example of an overriddensolution.

CROSSREFS

Adjacent-numbered pages:
BP565 BP566 BP567 BP568 BP569  *  BP571 BP572 BP573 BP574 BP575

KEYWORD

less, example, overriddensolution, experimental, funny, neither

WORLD

outline_or_fill_shape [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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