The On-Line Encyclopedia of Bongard Problems

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BP1077

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`

BP1088

Top piece can fit into bottom piece without leaving any overhangs vs. not so

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	COMMENTS	`The piece does not need to slide in from above, unlike the game Tetris.`
	CROSSREFS	`Adjacent-numbered pages: BP1083 BP1084 BP1085 BP1086 BP1087 * BP1089 BP1090 BP1091 BP1092 BP1093`
	KEYWORD	`perfect, pixelperfect`
	AUTHOR	`William B Holland`

BP1089

Equal number of black and white pixels vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1084 BP1085 BP1086 BP1087 BP1088 * BP1090 BP1091 BP1092 BP1093 BP1094`
	KEYWORD	`nice, precise, allsorted, boundingbox, right-null, perfect, pixelperfect, help, preciseworld, bordercontent, blackwhiteinvariant`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1093

"Inverted symmetry" present vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1088 BP1089 BP1090 BP1091 BP1092 * BP1094 BP1095 BP1096 BP1097 BP1098`
	KEYWORD	`nice, precise, allsorted, boundingbox, left-narrow, right-null, perfect, pixelperfect, preciseworld, bordercontent, blackwhiteinvariant`
	CONCEPT	`black_white_inversion (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1094

Convex hulls intersect vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1089 BP1090 BP1091 BP1092 BP1093 * BP1095 BP1096 BP1097 BP1098 BP1099`
	KEYWORD	`precise, perfect, unorderedpair`
	CONCEPT	`convex_hull (info \| search),` `overlap (info \| search)`
	AUTHOR	`Jago Collins`

BP1095

Angle of incidence equals angle of reflection vs. not

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	REFERENCE	`https://en.wikipedia.org/wiki/Specular_reflection` `https://en.wikipedia.org/wiki/Snooker`
	CROSSREFS	`Adjacent-numbered pages: BP1090 BP1091 BP1092 BP1093 BP1094 * BP1096 BP1097 BP1098 BP1099 BP1100`
	KEYWORD	`easy, nice, precise, allsorted, physics, perfect`
	AUTHOR	`Jago Collins`

BP1098

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`

BP1104

Vertically centered versus horizontally centered

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	COMMENTS	`It is easier to notice that the left examples are vertically centered than that the right examples are horizontally centered. - Aaron David Fairbanks, Dec 27 2022`
	CROSSREFS	`Adjacent-numbered pages: BP1099 BP1100 BP1101 BP1102 BP1103 * BP1105 BP1106 BP1107 BP1108 BP1109`
	KEYWORD	`easy, nice, precise, minimal, boundingbox, perfect, pixelperfect, traditional, finishedexamples, preciseworld, absoluteposition, unstableworld`
	CONCEPT	`center_bounding_box (info \| search),` `center (info \| search)`
	WORLD	`horizontal_line_segment [smaller \| same \| bigger]`
	AUTHOR	`Widad Dabbas`

BP1107

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`

BP1108

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

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

	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`

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