The On-Line Encyclopedia of Bongard Problems

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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

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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`

BP1238

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

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	CROSSREFS	`Adjacent-numbered pages: BP1233 BP1234 BP1235 BP1236 BP1237 * BP1239 BP1240 BP1241 BP1242 BP1243`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`closed_open (info \| search),` `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

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	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

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	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`

BP1234

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

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	CROSSREFS	`Adjacent-numbered pages: BP1229 BP1230 BP1231 BP1232 BP1233 * BP1235 BP1236 BP1237 BP1238 BP1239`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "diagonal"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1233

Different curves cross each other vs. curves only cross themselves (or do not cross at all).

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	CROSSREFS	`Adjacent-numbered pages: BP1228 BP1229 BP1230 BP1231 BP1232 * BP1234 BP1235 BP1236 BP1237 BP1238`
	KEYWORD	`notso, traditional`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `x-crossing (info \| search)`
	WORLD	`smooth_crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1232

Curves with at least one crossing vs. curves do not cross.

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	COMMENTS	`Based on BP30, "curve with exactly one self-crossing vs. curve without a self-crossing". This is just a slightly more general version.`
	CROSSREFS	`Adjacent-numbered pages: BP1227 BP1228 BP1229 BP1230 BP1231 * BP1233 BP1234 BP1235 BP1236 BP1237`
	EXAMPLE	`EX6881`
	KEYWORD	`stub, notso, traditional`
	CONCEPT	`x-crossing (info \| search),` `existence (info \| search)`
	WORLD	`crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1231

Bongard Problems where some information is left out from examples and they are only sorted on the side they seem to fit vs. other Bongard Problems.

BP1228

BP1229

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	COMMENTS	`Bongard Problems sorted left have the keyword "seemslike" on the OEBP.` `In a "seemslike" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "seemslike" BPs sound like "Seems like a ___ based on the information available vs. seems like a ___ based on the information available". The two sides are typically negations of one another (keyword notso).` `Since there is information missing, examples can only be sorted assuming they appear in a way that hints psychologically at what they actually are (see help).`
	CROSSREFS	`Although the rule sorting the underlying objects may be precise, the rule sorting the projections of the objects with lost information is fuzzy and subjective.` `See also left-couldbe (and right-couldbe), concerning situations in which the information given may be enough to determine when examples fail to satisfy a rule but is never enough to determine when they do satisfy the rule ("could be ___ vs. clearly is not"). In contrast to "seemslike" Bongard Problems, left-couldbe Bongard Problems can be precise; both evidence of fitting right and absence of evidence of fitting right is clear-cut, so no psychologically helpful hints (help) are needed.` `Adjacent-numbered pages: BP1226 BP1227 BP1228 BP1229 BP1230 * BP1232 BP1233 BP1234 BP1235 BP1236`
	KEYWORD	`meta (see left/right), links, keyword`
	AUTHOR	`Aaron David Fairbanks`

BP1230

Invariant under scaling by a certain amount vs. not.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1225 BP1226 BP1227 BP1228 BP1229 * BP1231 BP1232 BP1233 BP1234 BP1235`
	KEYWORD	`stub, notso, perfect, infinitedetail, left-couldbe, bordercontent, blackwhiteinvariant`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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