The On-Line Encyclopedia of Bongard Problems

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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	. . .

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

	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`

BP1114

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

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

	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`

BP1115

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

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

	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`

BP1116

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

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

	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`

BP1117

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

BP1108

BP1116

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

	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`

BP1118

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

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

	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`

BP1119

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

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

	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`

BP1120

No same-sized copies of self overlap vs. distinct same-sized copies overlap.

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

	COMMENTS	`With mathematical jargon:` `No distinct same-sized copies of self overlap on a subset with positive measure in the Hausdorff measure using the Hausdorff dimension.` `For a covering of a fractal by finitely many scaled down copies of itself, the condition of that no two have an intersection with positive measure is equivalent to the condition that the Hausdorff dimension coincides with the similarity dimension.` `(There is another similar condition in this context called the "open set condition" which implies this but is not equivalent. The open set condition is equivalent to the condition that the Hausdorff measure using the similarity dimension is nonzero.)`
	REFERENCE	`https://en.wikipedia.org/wiki/Hausdorff_dimension` `https://en.wikipedia.org/wiki/Open_set_condition`
	CROSSREFS	`Adjacent-numbered pages: BP1115 BP1116 BP1117 BP1118 BP1119 * BP1121 BP1122 BP1123 BP1124 BP1125`
	KEYWORD	`challenge, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1121

Bongard Problems that were added to the OEBP to be used as examples in particular meta-BPs vs. other Bongard Problems,

	BP570	BP868	BP915	BP1042	BP1043	BP1105
	BP1141	BP1150	BP1163	BP1168	BP1227

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

	COMMENTS	`Bongard Problems sorted left have the keyword "example" on the OEBP.` `Plea to the reader: We need a good counterexample for this Problem. Could you please make a good example of a Problem this meta BP would sort on its right? Don't forget to tag it appropriately. - Leo Crabbe, Dec 13 2021`
	CROSSREFS	`Adjacent-numbered pages: BP1116 BP1117 BP1118 BP1119 BP1120 * BP1122 BP1123 BP1124 BP1125 BP1126`
	KEYWORD	`meta (see left/right), links, keyword, oebp`
	AUTHOR	`Aaron David Fairbanks`

BP1122

Content of any square is an image of the whole panel vs. not so.

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

	CROSSREFS	`Similar to BP818.` `Adjacent-numbered pages: BP1117 BP1118 BP1119 BP1120 BP1121 * BP1123 BP1124 BP1125 BP1126 BP1127`
	KEYWORD	`nice, minimal, size, boundingbox, infinitedetail, preciseworld, absoluteposition`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

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