The On-Line Encyclopedia of Bongard Problems

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Tiled by finitely many smaller copies of itself (different sizes allowed) vs. not so.

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	COMMENTS	`These are sometimes called "irreptiles".`
	CROSSREFS	`See BP532 for the version with only one size of tile allowed.` `Adjacent-numbered pages: BP1114 BP1115 BP1116 BP1117 BP1118 * BP1120 BP1121 BP1122 BP1123 BP1124`
	KEYWORD	`hardsort, proofsrequired, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1118

Self-similar only scaled about one point vs. multiple centers of self-similarity.

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	COMMENTS	`There is only ever one such center of self-similarity or infinitely many.`
	CROSSREFS	`Adjacent-numbered pages: BP1113 BP1114 BP1115 BP1116 BP1117 * BP1119 BP1120 BP1121 BP1122 BP1123`
	KEYWORD	`nice, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1117

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

BP1108

BP1116

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	CROSSREFS	`Adjacent-numbered pages: BP1112 BP1113 BP1114 BP1115 BP1116 * BP1118 BP1119 BP1120 BP1121 BP1122`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "topological_density"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1116

Contains self somewhere within any area around any point within self vs. not so.

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	COMMENTS	`Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".` `The left hand side of this is a weaker condition than the left hand side of BP1241.`
	CROSSREFS	`Adjacent-numbered pages: BP1111 BP1112 BP1113 BP1114 BP1115 * BP1117 BP1118 BP1119 BP1120 BP1121`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1115

Fractals tile one another vs. not so (fractals are rather tiled by some combination of one another and themselves).

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	COMMENTS	`Rotations and reflections avoided in all examples for simplicity.`
	CROSSREFS	`Adjacent-numbered pages: BP1110 BP1111 BP1112 BP1113 BP1114 * BP1116 BP1117 BP1118 BP1119 BP1120`
	KEYWORD	`perfect, infinitedetail, unorderedpair`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1114

Fractals contain one another vs. only one contains the other.

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	CROSSREFS	`Adjacent-numbered pages: BP1109 BP1110 BP1111 BP1112 BP1113 * BP1115 BP1116 BP1117 BP1118 BP1119`
	KEYWORD	`perfect, infinitedetail, unorderedpair`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1113

Bongard Problems relating to the OEBP vs. Bongard Problems unrelated to the OEBP.

BP503	BP504	BP518	BP542	BP546	BP919
BP930	BP943	BP967	BP1113	BP1121	BP1125
BP1150	BP1174

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP10	BP11	BP12
BP13	BP14	BP15	BP16	BP17	BP18
BP19	BP20	BP21	BP22	BP23	BP24
BP25	BP26	BP27	BP28	BP29	BP30
BP31	BP32	BP33	BP34	BP35	. . .

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	COMMENTS	`Bongard Problems sorted left have the keyword "oebp" on the OEBP.` `Most Bongard Problems relating to the OEBP are meta.`
	CROSSREFS	`Adjacent-numbered pages: BP1108 BP1109 BP1110 BP1111 BP1112 * BP1114 BP1115 BP1116 BP1117 BP1118`
	KEYWORD	`notso, meta (see left/right), links, keyword, oebp, left-self, metameta`
	AUTHOR	`Leo Crabbe`

BP1112

"Stretch-dependent" Bongard Problems vs. Bongard Problems in which examples can be stretched (or compressed) along any axis without being sorted differently.

BP7	BP11	BP12	BP13	BP33	BP50
BP62	BP76	BP77	BP80	BP103	BP152
BP250	BP289	BP328	BP329	BP333	BP335
BP336	BP523	BP525	BP536	BP557	BP559
BP812	BP813	BP816	BP860	BP920	BP924
BP942	BP949	BP1011	BP1086	BP1145	. . .

BP1	BP5	BP15	BP31	BP45	BP98
BP157	BP240	BP322	BP327	BP330	BP331
BP332	BP348	BP363	BP367	BP368	BP369
BP389	BP809	BP810	BP851	BP853	BP911
BP966	BP977	BP992	BP1022	BP1094	BP1131
BP1135	BP1136

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "stretch" on the OEBP.` `If applying a scaling along one particular axis to the whole of any example can change its sorting the BP fits on the left side here. (For BPs with bounding boxes this means scaling and cropping, but without cutting out any detail.)`
	CROSSREFS	`Adjacent-numbered pages: BP1107 BP1108 BP1109 BP1110 BP1111 * BP1113 BP1114 BP1115 BP1116 BP1117`
	KEYWORD	`meta (see left/right), links, keyword, invariance`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1111

Bongard Problem requires solver to already be interpreting all examples in a specific way for the answer to seem simple vs. not so.

BP200	BP361	BP362	BP793	BP795	BP796
BP802	BP803	BP827	BP828	BP829	BP831
BP832	BP833	BP834	BP835	BP836	BP852
BP871	BP872	BP873	BP874	BP875	BP876
BP877	BP878	BP879	BP880	BP881	BP894
BP955	BP957	BP968	BP987	BP1024	. . .

BP1

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "assumesfamiliarity" on the OEBP.` `Sometimes all the examples in a Bongard Problem need to be interpreted a certain way for the Bongard Problem to make sense. Only once the representation is understood, the idea seems simple.` `For example, all meta Bongard Problems (Bongard Problems sorting other Bongard Problems) assume the solver interprets the examples as Bongard Problems.` `TO DO: Maybe it is best to stop putting the label "assumesfamiliarity" on all meta-Bongard Problems. There are so many of them. It may be better to only use the "assumesfamiliarity" keyword on meta-BPs for a further assumption than just that all examples are interpreted as Bongard Problems. - Aaron David Fairbanks, Feb 11 2021`
	CROSSREFS	`Many Bongard Problems in which all examples take the same format (keyword structure) assume the solver already knows how to read that format.` `Some Bongard Problems assume the solver will be able to understand symbolism that is consistent between examples (keyword consistentsymbols).` `Bongard Problems tagged math often assume the solver is familiar with a certain representation of a math idea.` `Adjacent-numbered pages: BP1106 BP1107 BP1108 BP1109 BP1110 * BP1112 BP1113 BP1114 BP1115 BP1116`
	EXAMPLE	`BP1032: The solution should really read "Assuming all images are Bongard Problems sorting each natural number left or right ..." This Bongard Problem makes sense to someone who has been solving a series of similar BPs, but otherwise there is no reason to automatically read a collection of numbers as standing for a larger collection of numbers.`
	KEYWORD	`fuzzy, meta (see left/right), links, keyword`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1110

The process that turns one object into the other is the same both ways vs. the process changes depending on which object is chosen as the starting point.

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	REFERENCE	`https://en.wikipedia.org/wiki/Duality_(mathematics)` `https://en.wikipedia.org/wiki/Involution_(mathematics)`
	CROSSREFS	`This is a special case of BP841 and a generalisation of BP822.` `Adjacent-numbered pages: BP1105 BP1106 BP1107 BP1108 BP1109 * BP1111 BP1112 BP1113 BP1114 BP1115`
	KEYWORD	`nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

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