The On-Line Encyclopedia of Bongard Problems

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White space in two circles maximum vs. white space in three circles maximum.

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	CROSSREFS	`Adjacent-numbered pages: BP1014 BP1015 BP1016 BP1017 BP1018 * BP1020 BP1021 BP1022 BP1023 BP1024`
	KEYWORD	`nice, precise, traditional`
	CONCEPT	`recursion_number (info \| search),` `separated_regions (info \| search),` `circle (info \| search),` `recursion (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`circles_cross [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Fractals contain one another vs. only one contains the other.

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	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`

Some similar figures vs. no similar figures.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.`
	CROSSREFS	`Adjacent-numbered pages: BP55 BP56 BP57 BP58 BP59 * BP61 BP62 BP63 BP64 BP65`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`similar_shape (info \| search),` `similar (info \| search)`
	WORLD	`outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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`

More white circles than black circles vs. at least as many black circles as white circles.

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	CROSSREFS	`See the twin BP1044.` `Adjacent-numbered pages: BP1041 BP1042 BP1043 BP1044 BP1045 * BP1047 BP1048 BP1049 BP1050 BP1051`
	KEYWORD	`precise, allsorted, spectrum, discrete, preciseworld`
	CONCEPT	`ratio (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Exponential increase vs. linear increase.

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	CROSSREFS	`Adjacent-numbered pages: BP387 BP388 BP389 BP390 BP391 * BP393 BP394 BP395 BP396 BP397`
	KEYWORD	`contributepairs, traditional`
	CONCEPT	`acceleration (info \| search),` `exponential (info \| search)`
	AUTHOR	`Jago Collins`

Two of the same object are enclosed in the same space (there is a path between them) vs. not so.

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	COMMENTS	`An "object" is everything within some black boundary.`
	CROSSREFS	`See BP1071 for a version with only squares and with infinite nesting allowed.` `Adjacent-numbered pages: BP972 BP973 BP974 BP975 BP976 * BP978 BP979 BP980 BP981 BP982`
	KEYWORD	`nice, precise, allsorted, creativeexamples, traditional`
	CONCEPT	`separated_regions (info \| search),` `identical (info \| search),` `recursion (info \| search),` `imagined_line_or_curve (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Image conceptually relates to the golden ratio/Fibonacci numbers versus not so.

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	CROSSREFS	`BP800 is the metaconcept page for this concept.` `Adjacent-numbered pages: BP792 BP793 BP794 BP795 BP796 * BP798 BP799 BP800 BP801 BP802`
	KEYWORD	`abstract, math, concept, experimental`
	CONCEPT	`golden_ratio (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Counterclockwise along the curve following the arrow vs. clockwise along the curve following the arrow.

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	CROSSREFS	`Adjacent-numbered pages: BP358 BP359 BP360 BP361 BP362 * BP364 BP365 BP366 BP367 BP368`
	KEYWORD	`easy, nice, dual, handed, leftright, updown, gap, traditional`
	CONCEPT	`arrow (info \| search),` `turn_orientation (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Quadrilateral that is nearly a triangle vs. typical quadrilateral.

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	CROSSREFS	`Adjacent-numbered pages: BP155 BP156 BP157 BP158 BP159 * BP161 BP162 BP163 BP164 BP165`
	KEYWORD	`perfect, traditional`
	CONCEPT	`imperfection_small (info \| search),` `number (info \| search),` `triangle (info \| search)`
	WORLD	`Multiple options: [smaller \| same \| bigger], quadrilateral_outline [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

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