The On-Line Encyclopedia of Bongard Problems

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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`

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`

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`

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`

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`

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`

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`

BP1123

Can be cut into tiles forming a checkerboard pattern vs. not so.

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	COMMENTS	`All examples in this Problem are grids consisting of two objects.`
	CROSSREFS	`Adjacent-numbered pages: BP1118 BP1119 BP1120 BP1121 BP1122 * BP1124 BP1125 BP1126 BP1127 BP1128`
	EXAMPLE	`EX9124 shows a 9 square by 9 square grid. Take each tile to be 3 squares by 3 squares; there is a 3 tile by 3 tile checkerboard pattern. (One of these tiles is itself a checkerboard pattern; the other is all black squares.)`
	KEYWORD	`hard, nice, precise, allsorted, hardsort, grid, miniworlds`
	AUTHOR	`Jago Collins`

BP1131

One shape can be totally obscured by the other vs. neither shape can be obscured.

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	COMMENTS	`Rotation of shapes is not required for any left-hand panels, but it should not change any example's sorting if it is considered.`
	CROSSREFS	`Adjacent-numbered pages: BP1126 BP1127 BP1128 BP1129 BP1130 * BP1132 BP1133 BP1134 BP1135 BP1136`
	KEYWORD	`nice, precise, allsorted, pixelperfect, unorderedpair`
	CONCEPT	`overlap (info \| search)`
	WORLD	`2_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1132

Circle that passes through points is contained within bounding box vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1127 BP1128 BP1129 BP1130 BP1131 * BP1133 BP1134 BP1135 BP1136 BP1137`
	KEYWORD	`precise, allsorted, boundingbox, hardsort, preciseworld, absoluteposition`
	CONCEPT	`circle (info \| search),` `imagined_entity (info \| search)`
	WORLD	`three_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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