The On-Line Encyclopedia of Bongard Problems

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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`

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.

BP1242

BP1244

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

	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`

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.

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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`

BP1239

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

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

	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`

BP1238

Fractal with hole vs. fractal with no hole (simply connected).

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

	CROSSREFS	`Adjacent-numbered pages: BP1233 BP1234 BP1235 BP1236 BP1237 * BP1239 BP1240 BP1241 BP1242 BP1243`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`existence (info \| search),` `fractal (info \| search),` `hole (info \| search),` `loop (info \| search)`
	WORLD	`connected_fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1236

Bongard Problem with solution relating to concept: connected component vs. Bongard Problem unrelated to this concept.

BP1100

BP1237

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

	CROSSREFS	`Adjacent-numbered pages: BP1231 BP1232 BP1233 BP1234 BP1235 * BP1237 BP1238 BP1239 BP1240 BP1241`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "connected_component"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1235

Bongard Problem with solution relating to concept: distingushing between distinct curves that cross vs. Bongard Problem unrelated to this concept.

BP31	BP190	BP391	BP560	BP562	BP576
BP788	BP932	BP1099	BP1100	BP1101	BP1102
BP1109	BP1233

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

	CROSSREFS	`Adjacent-numbered pages: BP1230 BP1231 BP1232 BP1233 BP1234 * BP1236 BP1237 BP1238 BP1239 BP1240`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "distinguishing_crossing_curves"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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