The On-Line Encyclopedia of Bongard Problems

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Every nonempty region has two boxes vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1063 BP1064 BP1065 BP1066 BP1067 * BP1069 BP1070 BP1071 BP1072 BP1073`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Infinitely many branches vs. finitely many branches.

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	CROSSREFS	`Adjacent-numbered pages: BP1064 BP1065 BP1066 BP1067 BP1068 * BP1070 BP1071 BP1072 BP1073 BP1074`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Dead end vs. no dead ends.

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	CROSSREFS	`Adjacent-numbered pages: BP1065 BP1066 BP1067 BP1068 BP1069 * BP1071 BP1072 BP1073 BP1074 BP1075`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Two of the same kind within in one region vs. not so.

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	CROSSREFS	`See BP977 for a version without infinite nesting and other drawings than boxes.` `Adjacent-numbered pages: BP1066 BP1067 BP1068 BP1069 BP1070 * BP1072 BP1073 BP1074 BP1075 BP1076`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

All regions have the same number of boxes vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1072 BP1073 BP1074 BP1075 BP1076 * BP1078 BP1079 BP1080 BP1081 BP1082`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Images of Bongard Problems about images of Bongard Problems vs. images of Bongard Problems not including images of Bongard Problems.

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	CROSSREFS	`See BP537 for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP1079 BP1080 BP1081 BP1082 BP1083 * BP1085 BP1086 BP1087 BP1088 BP1089`
	KEYWORD	`meta (see left/right), miniproblems, perfect, infinitedetail, presentationinvariant`
	WORLD	`boxes_bpimage [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

Concave shapes whose cavities are similar to the shape vs. concave shape whose cavities are not similar to the shape.

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	COMMENTS	`"I am agnostic on whether to let this world include examples such as EX8932, where pixelation is used, or examples such as suggested by EX8928 similar to the "Topologist's Comb" (link in references) which are not locally path-connected. These two examples were provided by Aaron David Fairbanks." - Jago Collins 28th January 2021`
	REFERENCE	`https://en.wikipedia.org/wiki/Similarity_(geometry)` `https://en.wikipedia.org/wiki/Self-similarity` `https://en.wikipedia.org/wiki/Comb_space`
	CROSSREFS	`Adjacent-numbered pages: BP1093 BP1094 BP1095 BP1096 BP1097 * BP1099 BP1100 BP1101 BP1102 BP1103`
	EXAMPLE	`A circle with a circle cut out of it does not fit left, because with the circle cut out of it, our shape is no longer a circle.`
	KEYWORD	`stub, precise, allsorted, left-narrow, perfect, infinitedetail`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Jago Collins`

Contains smaller copy of self with black and white inverted vs. not so.

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	COMMENTS	`There are various problematic cases left out. Are black and white to be inverted within a fractal's convex hull or its outermost outline?` `Must this outline be preserved around the smaller inverted version of the fractal, or is it allowed to bleed into other white areas?` `No examples have been included in this Bongard Problem whose placement depends on these questions.`
	CROSSREFS	`Adjacent-numbered pages: BP1102 BP1103 BP1104 BP1105 BP1106 * BP1108 BP1109 BP1110 BP1111 BP1112`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`black_white_inversion (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Solid chunk of black space in neighborhood of any point of the fractal vs. solid chunk of white space in any neighborhood.

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	CROSSREFS	`Adjacent-numbered pages: BP1103 BP1104 BP1105 BP1106 BP1107 * BP1109 BP1110 BP1111 BP1112 BP1113`
	KEYWORD	`right-null, perfect, infinitedetail, assumesfamiliarity, neither`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

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