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BP1253

Text strings vs. images of text strings

WWWWWWW

____hem

image

joym

жю

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1248 BP1249 BP1250 BP1251 BP1252 * BP1254`
	KEYWORD	`experimental`
	AUTHOR	`Leo Crabbe`

BP1252

No entirely white paths from one side to another vs. one can find such a path.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1247 BP1248 BP1249 BP1250 BP1251 * BP1253 BP1254`
	KEYWORD	`precise, allsorted, notso, blackwhite`
	AUTHOR	`Leo Crabbe`

BP1249

Any straight path will hit a black region vs. not so.

(edit; present; nest [left/right]; search; history)

	REFERENCE	`https://en.wikipedia.org/wiki/Opaque_set`
	CROSSREFS	`Adjacent-numbered pages: BP1244 BP1245 BP1246 BP1247 BP1248 * BP1250 BP1251 BP1252 BP1253 BP1254`
	KEYWORD	`notso, blackwhite, right-null, perfect`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1248

No straight path passes from a white region to a grey one, then to white again (without hitting black) vs. such a path exists.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1243 BP1244 BP1245 BP1246 BP1247 * BP1249 BP1250 BP1251 BP1252 BP1253`
	KEYWORD	`precise, allsorted, unwordable, notso, perfect`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1247

No straight path from one side of the panel to the other passes through the grey shape without hitting a black region vs. such a path exists.

(edit; present; nest [left/right]; search; history)

	REFERENCE	`https://en.wikipedia.org/wiki/Opaque_set`
	CROSSREFS	`Adjacent-numbered pages: BP1242 BP1243 BP1244 BP1245 BP1246 * BP1248 BP1249 BP1250 BP1251 BP1252`
	KEYWORD	`precise, allsorted, unwordable, notso`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1246

Any symmetry exhibited by some non-empty subset of the objects is also a symmetry of the whole thing vs. not so.

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	COMMENTS	`In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.`
	CROSSREFS	`See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.` `Adjacent-numbered pages: BP1241 BP1242 BP1243 BP1244 BP1245 * BP1247 BP1248 BP1249 BP1250 BP1251`
	KEYWORD	`precise, allsorted, unwordable, notso, traditional`
	CONCEPT	`self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1245

When two players alternate coloring regions, either can force connection from top edge to bottom edge vs. either can force connection from left edge to right edge.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1240 BP1241 BP1242 BP1243 BP1244 * BP1246 BP1247 BP1248 BP1249 BP1250`
	KEYWORD	`hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired`
	AUTHOR	`Aaron David Fairbanks`

BP1244

Tiled by self-tiling fractal vs. not

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	COMMENTS	`Proofs are still needed for examples fitting right.` `EX9875 is tiled by Sierpinski triangles, but this requires the Sierpinski triangle tiles' bounding triangles to overlap.`
	CROSSREFS	`Self-tiling fractals (BP532^left) are all sorted left.` `Adjacent-numbered pages: BP1239 BP1240 BP1241 BP1242 BP1243 * BP1245 BP1246 BP1247 BP1248 BP1249`
	KEYWORD	`notso, perfect, infinitedetail, missingproofs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1242

Tiled by pair of fractals including itself such that both tile the other vs. tiled by pair of fractals including itself such that the other tiles itself.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Proofs still needed that all the examples on the left hand side cannot fit on the right hand side as well, and that EX9881 cannot fit on the left hand side as well.`
	CROSSREFS	`The left hand side implies the left hand side of BP1116.` `The right hand side does not imply the right hand side of BP1116. (EX9881 is meant to be a counterexample.)` `Adjacent-numbered pages: BP1237 BP1238 BP1239 BP1240 BP1241 * BP1243 BP1244 BP1245 BP1246 BP1247`
	KEYWORD	`unwordable, overriddensolution, perfect, infinitedetail, both, missingproofs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1241

Any point contained in (arbitrarily) smaller version of self vs. not so.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.` `It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)` `The left hand side of this is a stronger condition than the left hand side of BP1116.`
	CROSSREFS	`Adjacent-numbered pages: BP1236 BP1237 BP1238 BP1239 BP1240 * BP1242 BP1243 BP1244 BP1245 BP1246`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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