The On-Line Encyclopedia of Bongard Problems

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Concave shape vs. convex shape.

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	CROSSREFS	`BP4 is the same solution (flipped) but without the distracting dots (and also with some shapes filled in black and/or curvy instead of just polygon outlines).` `Adjacent-numbered pages: BP131 BP132 BP133 BP134 BP135 * BP137 BP138 BP139 BP140 BP141`
	KEYWORD	`noisy, ignoreimperfections, traditional`
	CONCEPT	`concave_convex_angle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Black figure is a triangle vs. black figure is a circle.

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	COMMENTS	`All small squares appearing in this problem are axis-aligned.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.`
	CROSSREFS	`Adjacent-numbered pages: BP20 BP21 BP22 BP23 BP24 * BP26 BP27 BP28 BP29 BP30`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `texture (info \| search),` `triangle (info \| search)`
	WORLD	`circle_square_eq-tri_small_outlines_one_fill [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Ghost shape is square vs. Ghost shape is rectangular.

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	CROSSREFS	`Adjacent-numbered pages: BP292 BP293 BP294 BP295 BP296 * BP298 BP299 BP300 BP301 BP302`
	KEYWORD	`traditional`
	CONCEPT	`absence_as_presence (info \| search),` `ghost (info \| search)`
	AUTHOR	`"Lewis"`

Contains smaller copy of itself vs. doesn't.

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	CROSSREFS	`Adjacent-numbered pages: BP528 BP529 BP530 BP531 BP532 * BP534 BP535 BP536 BP537 BP538`
	EXAMPLE	`A smaller copy of EX6409 (the black area) can be located within itself, but some of the white space inside it is not retained in this smaller copy.`
	KEYWORD	`perfect, infinitedetail, contributepairs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_built_from_self_tile_fractals [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Imperfectly drawn shapes vs. perfectly drawn shapes.

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	CROSSREFS	`Adjacent-numbered pages: BP907 BP908 BP909 BP910 BP911 * BP913 BP914 BP915 BP916 BP917`
	KEYWORD	`perfect, contributepairs`
	CONCEPT	`curve_texture (info \| search)`
	WORLD	`zoom in right (shape_outline)`
	AUTHOR	`Leo Crabbe`

Straight line joining the curve ends does not cut the curve vs. straight line joining the curve ends intersects the curve.

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	CROSSREFS	`Adjacent-numbered pages: BP235 BP236 BP237 BP238 BP239 * BP241 BP242 BP243 BP244 BP245`
	KEYWORD	`traditional`
	CONCEPT	`x-crossing (info \| search),` `line_or_curve_endpoint (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Matthew J. Howells`

Concave shapes with concave cavities vs. convex cavities

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	COMMENTS	`All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.`
	CROSSREFS	`Adjacent-numbered pages: BP987 BP988 BP989 BP990 BP991 * BP993 BP994 BP995 BP996 BP997`
	KEYWORD	`nice, precise, perfect, traditional`
	CONCEPT	`recursion_number (info \| search),` `recursion (info \| search)`
	WORLD	`concave_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

All curves spiral counterclockwise, starting from maximum curvature vs. all curves spiral clockwise, starting from maximum curvature.

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	CROSSREFS	`Adjacent-numbered pages: BP203 BP204 BP205 BP206 BP207 * BP209 BP210 BP211 BP212 BP213`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `turn_orientation (info \| search),` `tracing_line_or_curve (info \| search),` `rotational_direction (info \| search),` `direction (info \| search)`
	AUTHOR	`Giuseppe Insana`

Indentation on protrusion vs. indentation on indentation.

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	CROSSREFS	`Adjacent-numbered pages: BP124 BP125 BP126 BP127 BP128 * BP130 BP131 BP132 BP133 BP134`
	KEYWORD	`traditional`
	CONCEPT	`indentation (info \| search),` `protrusion (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

If two nodes are linked, they are each linked to a different number of nodes vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Highly_irregular_graph`
	CROSSREFS	`Adjacent-numbered pages: BP1278 BP1279 BP1280 BP1281 BP1282 * BP1284 BP1285 BP1286 BP1287 BP1288`
	CONCEPT	`graph (info \| search)`
	AUTHOR	`Leo Crabbe`

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