The On-Line Encyclopedia of Bongard Problems

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Line segments linking same-coloured dots would intersect vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1012 BP1013 BP1014 BP1015 BP1016 * BP1018 BP1019 BP1020 BP1021 BP1022`
	KEYWORD	`easy, nice, precise, allsorted, perfect, traditional, finishedexamples, preciseworld`
	CONCEPT	`lines_coincide (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	AUTHOR	`Leo Crabbe`

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`

No same-sized copies of self overlap vs. distinct same-sized copies overlap.

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	COMMENTS	`With mathematical jargon:` `No distinct same-sized copies of self overlap on a subset with positive measure in the Hausdorff measure using the Hausdorff dimension.` `For a covering of a fractal by finitely many scaled down copies of itself, the condition of that no two have an intersection with positive measure is equivalent to the condition that the Hausdorff dimension coincides with the similarity dimension.` `(There is another similar condition in this context called the "open set condition" which implies this but is not equivalent. The open set condition is equivalent to the condition that the Hausdorff measure using the similarity dimension is nonzero.)`
	REFERENCE	`https://en.wikipedia.org/wiki/Hausdorff_dimension` `https://en.wikipedia.org/wiki/Open_set_condition`
	CROSSREFS	`Adjacent-numbered pages: BP1115 BP1116 BP1117 BP1118 BP1119 * BP1121 BP1122 BP1123 BP1124 BP1125`
	KEYWORD	`challenge, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

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