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`

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`

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`

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`

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.

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

	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`

BP1109

Considering only the ways they are connected, anything that can be said about a given edge can be said about every other edge vs. not so.

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	REFERENCE	`https://mathworld.wolfram.com/Edge-TransitiveGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1104 BP1105 BP1106 BP1107 BP1108 * BP1110 BP1111 BP1112 BP1113 BP1114`
	KEYWORD	`precise, allsorted, notso, math, left-narrow, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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`

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`

BP1105

Maze object features multiple branching paths vs. one path in maze object.

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

	COMMENTS	`This was created as an example of a distractingworld Bongard Problem. Each example shows a distractingly detailed scene, irrelevant to the solution.` `Despite this distraction, the keyword noisy does not fit this Bongard Problem because only details relevant to the solution change between examples.`
	CROSSREFS	`Adjacent-numbered pages: BP1100 BP1101 BP1102 BP1103 BP1104 * BP1106 BP1107 BP1108 BP1109 BP1110`
	KEYWORD	`easy, nice, arbitrary, example, distractingworld, experimental`
	AUTHOR	`Aaron David Fairbanks`

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