The On-Line Encyclopedia of Bongard Problems

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Fractal topologically closed (each white point has a neighborhood of pure white surrounding it) vs. not

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	COMMENTS	`It isn't possible to unambiguously communicate whether or not a few specific points are missing.`
	CROSSREFS	`Adjacent-numbered pages: BP1234 BP1235 BP1236 BP1237 BP1238 * BP1240 BP1241 BP1242 BP1243 BP1244`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1241

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

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	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`

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	`local_global (info \| search),` `self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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.

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	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`

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.

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	CROSSREFS	`Any small amount of convexity along the grey border will cause an example to fit right.` `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`

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, bordercontent`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1252

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

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	COMMENTS	`The left-sorted patterns connect all four corners with a single black region. - Rhodri Prysor, Oct 16 2024`
	CROSSREFS	`Adjacent-numbered pages: BP1247 BP1248 BP1249 BP1250 BP1251 * BP1253 BP1254 BP1255 BP1256 BP1257`
	KEYWORD	`precise, allsorted, notso, blackwhite, right-null, bordercontent`
	AUTHOR	`Leo Crabbe`

BP1258

It is possible to deduce the contents of any square from the rest vs. it is not.

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	CROSSREFS	`BP979 is very similar: whether a particular square can be deduced from the rest.` `Adjacent-numbered pages: BP1253 BP1254 BP1255 BP1256 BP1257 * BP1259 BP1260 BP1261 BP1262 BP1263`
	KEYWORD	`notso, rules, grid, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `choice (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1259

Rule is the same for rows as it is for columns vs. not

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	CROSSREFS	`All examples on the left are chosen so that rotating or flipping the grid in any way would result in a grid satisfying the same rule.` `Adjacent-numbered pages: BP1254 BP1255 BP1256 BP1257 BP1258 * BP1260 BP1261 BP1262 BP1263 BP1264`
	KEYWORD	`notso, rules, grid, miniworlds`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1261

Exactly one connected white region for each possible way shapes can overlap vs. not so.

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	COMMENTS	`All left-sorted examples have 2^n distinct white regions (counting the background), where n is the number of shapes in the image.`
	REFERENCE	`https://en.wikipedia.org/wiki/Venn_diagram`
	CROSSREFS	`Similar solution to BP1262, except there overlaps do not have to be unique.` `Adjacent-numbered pages: BP1256 BP1257 BP1258 BP1259 BP1260 * BP1262 BP1263 BP1264 BP1265 BP1266`
	KEYWORD	`notso, left-narrow, left-null, perfect`
	CONCEPT	`exists_one (info \| search)`
	AUTHOR	`Leo Crabbe`

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