The On-Line Encyclopedia of Bongard Problems

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Bongard Problems such that potential left examples can intuitively be put in bijection with potential right examples vs. other Bongard Problems.

BP7	BP8	BP19	BP36	BP43	BP45
BP54	BP55	BP63	BP64	BP67	BP95
BP106	BP109	BP157	BP158	BP180	BP196
BP197	BP211	BP234	BP278	BP279	BP286
BP313	BP337	BP357	BP363	BP372	BP513
BP514	BP515	BP516	BP517	BP793	. . .

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	COMMENTS	`This is the keyword "dual" on the OEBP.` `Given an example there is some way to "flip sides" by altering it. The left-to-right and right-to-left transformations should be inverses.` `It is not required that there only be one such transformation. For example, for many handed Bongard Problem, flipping an example over any axis will reliably switch its sorting.` `It is not required that every left example must have its corresponding right example uploaded on the OEBP nor vice versa. See the keyword contributepairs for the BPs the OEBP advises users upload left and right examples for in pairs.`
	CROSSREFS	`Adjacent-numbered pages: BP529 BP530 BP531 BP532 BP533 * BP535 BP536 BP537 BP538 BP539`
	KEYWORD	`meta (see left/right), links, keyword, sideless`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP535

Visual Bongard Problems such that flipping over the vertical axis (left/right) can switch an example's side vs. visual Bongard Problems whose examples' sorting doesn't change under such a transformation.

BP8	BP43	BP67	BP109	BP207	BP234
BP278	BP279	BP313	BP337	BP357	BP363
BP372	BP793	BP795	BP796	BP805	BP830
BP881	BP931	BP955	BP961	BP971	BP1008
BP1014	BP1024	BP1025	BP1027	BP1028	BP1029
BP1030	BP1031	BP1032	BP1033	BP1034	. . .

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	COMMENTS	`Left examples have the keyword "leftright" on the OEBP.`
	CROSSREFS	`See updown.` `All "leftright" Bongard Problems are handed.` `Adjacent-numbered pages: BP530 BP531 BP532 BP533 BP534 * BP536 BP537 BP538 BP539 BP540`
	KEYWORD	`meta (see left/right), links, keyword, sideless, invariance`
	WORLD	`handed_visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP552

Orientation-dependent Bongard Problems vs. orientation-independent visual Bongard Problems.

BP7	BP8	BP16	BP36	BP43	BP54
BP55	BP63	BP67	BP106	BP109	BP199
BP207	BP234	BP278	BP279	BP286	BP313
BP337	BP363	BP372	BP793	BP795	BP796
BP805	BP830	BP881	BP896	BP931	BP955
BP961	BP971	BP972	BP1008	BP1014	. . .

	BP1	BP2	BP3	BP4	BP5	BP6
	BP986	BP1197	BP1199	BP1200

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	COMMENTS	`Left examples have the keyword "handed" on the OEBP.` `If mirroring any example along the any axis can change its sorting the BP is "handed."` `Note that BPs about comparing orientation between multiple things in one example fit on the right side.`
	CROSSREFS	`See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.` `The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.` `Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.` `Adjacent-numbered pages: BP547 BP548 BP549 BP550 BP551 * BP553 BP554 BP555 BP556 BP557`
	KEYWORD	`meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger] zoom in left (handed_visualbp)`
	AUTHOR	`Aaron David Fairbanks`

BP657

Bongard Problem with solution relating to concept: left / right vs. Bongard Problem unrelated to this concept.

	BP8	BP63	BP67	BP68	BP191	BP234
	BP279	BP280	BP339

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	CROSSREFS	`Adjacent-numbered pages: BP652 BP653 BP654 BP655 BP656 * BP658 BP659 BP660 BP661 BP662`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "left_right"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP659

Bongard Problem with solution relating to concept: length of lines or curves vs. Bongard Problem unrelated to this concept.

BP14	BP79	BP80	BP103	BP112	BP131
BP151	BP155	BP176	BP235	BP237	BP239
BP241	BP243	BP256	BP257	BP279	BP280
BP314	BP328	BP939

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

	CROSSREFS	`Adjacent-numbered pages: BP654 BP655 BP656 BP657 BP658 * BP660 BP661 BP662 BP663 BP664`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "length_line_or_curve"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP936

Bongard Problem with solution relating to concept: area (geometry) vs. Bongard Problem unrelated to this concept.

BP279

BP935

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	CROSSREFS	`Adjacent-numbered pages: BP931 BP932 BP933 BP934 BP935 * BP937 BP938 BP939 BP940 BP941`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "area"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP947

BPs where users are advised to only upload images in which the pixelation is not misleading vs. other "perfect" Bongard Problems that use pixelated images to closely approximate the actual intended shapes.

BP1	BP31	BP210	BP211	BP217	BP279
BP321	BP324	BP325	BP335	BP341	BP367
BP386	BP523	BP548	BP859	BP860	BP861
BP892	BP920	BP934	BP935	BP966	BP1008
BP1088	BP1089	BP1090	BP1093	BP1104	BP1131
BP1156	BP1161	BP1168	BP1183

	BP344	BP559	BP564	BP912	BP937	BP949
	BP965

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	COMMENTS	`Left examples have the keyword "pixelperfect" on the OEBP.` `All examples here are perfect Bongard Problems. That is, subtle imperfections in images are meant to be considered.` `When a Problem is tagged with "pixelperfect", users are reminded to make sure they do not upload images such that taking the pixelation into account would affect the sorting of that example. That is, the zoomed-in jagged blocky version of the picture should still fit the solution.` `For example, in the examples of BP335, which is about tessellation, the pixels interlock properly.`
	CROSSREFS	`Stable Bongard Problems are generally pixelperfect.` `Adjacent-numbered pages: BP942 BP943 BP944 BP945 BP946 * BP948 BP949 BP950 BP951 BP952`
	KEYWORD	`meta (see left/right), links, keyword, instruction`
	WORLD	`perfect_bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1194

Bongard Problems listed in Harry E. Foundalis's collection vs. not.

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	. . .

	BP501	BP503	BP504	BP505	BP506	BP507
	BP508	BP509	BP510	BP1194

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

	COMMENTS	`Alternatively, BP pages on the OEBP with number less than or equal to 394 vs. other BP pages.`
	REFERENCE	`https://www.foundalis.com/res/bps/bpidx.htm`
	CROSSREFS	`Adjacent-numbered pages: BP1189 BP1190 BP1191 BP1192 BP1193 * BP1195 BP1196 BP1197 BP1198 BP1199`
	EXAMPLE	`Foundalis's collection includes all Bongard Problems by Bongard.`
	KEYWORD	`meta (see left/right), links, right-self, time`
	AUTHOR	`Aaron David Fairbanks`

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