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`

BP1240

Contains an un-nested white rectangle vs doesn't

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	CROSSREFS	`Adjacent-numbered pages: BP1235 BP1236 BP1237 BP1238 BP1239 * BP1241 BP1242 BP1243 BP1244 BP1245`
	CONCEPT	`existence (info \| search)`
	AUTHOR	`Leo Crabbe`

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`

BP1242

Meta Bongard Problems of the form "would sort [specific example] left vs. would sort [specific example] right" vs. other meta Bongard Problems.

BP567

BP1073

BP1076

BP1160

BP1242

?
BP517

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "testexample" on the OEBP.` `BP517 ("sorts self left vs. sorts self right") does not quite fit left; it is about the sorting of a specific example, but a different example for every Bongard Problem.`
	CROSSREFS	`testexample implies side.` `Adjacent-numbered pages: BP1237 BP1238 BP1239 BP1240 BP1241 * BP1243 BP1244 BP1245 BP1246 BP1247`
	KEYWORD	`meta (see left/right), links, keyword, right-self, metameta, left-it`
	WORLD	`linksbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1243

Bongard Problems on the OEBP with certain examples that have not yet been proved to fit where they are currently sorted vs. Bongard Problems in which all included examples have been proved to fit where they are.

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	COMMENTS	`Bongard Problems sorted left have the keyword "missingproofs" on the OEBP.` `This is an administrative keyword to help us keep track of what Bongard Problems we still need to check for correctness.` `The description should indicate which examples are still in need of checking. Once proofs are found, the keyword "missingproofs" can be removed.` `The keyword noproofs is similar. The difference is whether we want/expect to find proofs.`
	CROSSREFS	`Bongard Problems tagged "missingproofs" should necessarily be hardsort.` `Adjacent-numbered pages: BP1238 BP1239 BP1240 BP1241 BP1242 * BP1244 BP1245 BP1246 BP1247 BP1248`
	KEYWORD	`meta (see left/right), links, keyword, instruction, time`
	AUTHOR	`Aaron David Fairbanks`

BP1244

Bongard Problem with solution relating to concept: local global vs. Bongard Problem unrelated to this concept.

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	CROSSREFS	`Adjacent-numbered pages: BP1239 BP1240 BP1241 BP1242 BP1243 * BP1245 BP1246 BP1247 BP1248 BP1249`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "local_global"`
	WORLD	`bp [smaller \| same \| bigger]`
	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)

	REFERENCE	`https://en.wikipedia.org/wiki/Hex_(board_game)`
	CROSSREFS	`Adjacent-numbered pages: BP1240 BP1241 BP1242 BP1243 BP1244 * BP1246 BP1247 BP1248 BP1249 BP1250`
	KEYWORD	`hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired, bordercontent`
	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.

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

	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.

(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`

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	`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`

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