The On-Line Encyclopedia of Bongard Problems

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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.

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	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`

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`

BP1102

Nodes share the same edge connections as the vertices of a cube vs. not so.

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	REFERENCE	`https://mathworld.wolfram.com/CubicalGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1097 BP1098 BP1099 BP1100 BP1101 * BP1103 BP1104 BP1105 BP1106 BP1107`
	KEYWORD	`precise, allsorted, arbitrary, help, preciseworld`
	CONCEPT	`graph (info \| search),` `cube (info \| search),` `distinguishing_crossing_curves (info \| search),` `topological_transformation (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1101

Each node is connected to the same number of nodes by straight lines vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Regular_graph`
	CROSSREFS	`Any left example of BP1099 will be a left example for this BP.` `Adjacent-numbered pages: BP1096 BP1097 BP1098 BP1099 BP1100 * BP1102 BP1103 BP1104 BP1105 BP1106`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1100

There is a path between any two nodes vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Graph_theory` `https://en.wikipedia.org/wiki/Connectivity_(graph_theory)`
	CROSSREFS	`Adjacent-numbered pages: BP1095 BP1096 BP1097 BP1098 BP1099 * BP1101 BP1102 BP1103 BP1104 BP1105`
	KEYWORD	`precise, allsorted, world, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `connected_component (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left (connected_graph) \| zoom in right (disconnected_graph)`
	AUTHOR	`Leo Crabbe`

BP1099

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

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	REFERENCE	`https://en.wikipedia.org/wiki/Vertex-transitive_graph`
	CROSSREFS	`Adjacent-numbered pages: BP1094 BP1095 BP1096 BP1097 BP1098 * BP1100 BP1101 BP1102 BP1103 BP1104`
	KEYWORD	`precise, allsorted, notso, math, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

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`

BP1097

"Fault line" present vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1092 BP1093 BP1094 BP1095 BP1096 * BP1098 BP1099 BP1100 BP1101 BP1102`
	KEYWORD	`nice, precise, notso, left-finite, right-finite, preciseworld`
	AUTHOR	`Jago Collins`

BP1096

Line between ends intersects symbol vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1091 BP1092 BP1093 BP1094 BP1095 * BP1097 BP1098 BP1099 BP1100 BP1101`
	WORLD	`arial_font_centered_connected_symbol_two_ends [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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