The On-Line Encyclopedia of Bongard Problems

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BP531

Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself.

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	COMMENTS	`More specifically, all left examples shown in this Problem have Hausdorff dimension log2(3) while all right examples have Hausdorff dimension log3(5).` `Left examples can tile themselves by any power of 3 smaller same-sized copies of themselves while right examples can tile themselves by any power of 5 smaller same-sized copies of themselves.` `Homage to Bongard's original three versus five Problems.`
	CROSSREFS	`Adjacent-numbered pages: BP526 BP527 BP528 BP529 BP530 * BP532 BP533 BP534 BP535 BP536`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `three (info \| search),` `five (info \| search)`
	WORLD	`fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP217

Totally black lines vs. lines with white specks.

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	CROSSREFS	`Adjacent-numbered pages: BP212 BP213 BP214 BP215 BP216 * BP218 BP219 BP220 BP221 BP222`
	KEYWORD	`perfect, pixelperfect`
	CONCEPT	`curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP225

Low contrast (no fully black region) vs. high contrast (at least one fully black region).

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	CROSSREFS	`Adjacent-numbered pages: BP220 BP221 BP222 BP223 BP224 * BP226 BP227 BP228 BP229 BP230`
	KEYWORD	`nice, traditional, dithering`
	CONCEPT	`contrast (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP186

Object made of objects vs. object made of objects made of objects.

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	CROSSREFS	`Adjacent-numbered pages: BP181 BP182 BP183 BP184 BP185 * BP187 BP188 BP189 BP190 BP191`
	KEYWORD	`traditional`
	CONCEPT	`recursion (info \| search),` `cluster (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP1233

Different curves cross each other vs. curves only cross themselves (or do not cross at all).

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	CROSSREFS	`Adjacent-numbered pages: BP1228 BP1229 BP1230 BP1231 BP1232 * BP1234 BP1235 BP1236 BP1237 BP1238`
	KEYWORD	`notso, traditional`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `x-crossing (info \| search)`
	WORLD	`smooth_crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP952

Images of Bongard Problems about images of Bongard Problems about images of Bongard Problems vs. images of Bongard Problems not including images of Bongard Problems including images of Bongard Problems.

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	CROSSREFS	`See BP547 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Any left example in this BP will be a left example for BP1084.` `Adjacent-numbered pages: BP947 BP948 BP949 BP950 BP951 * BP953 BP954 BP955 BP956 BP957`
	KEYWORD	`meta (see left/right), miniproblems, funny, presentationinvariant`
	CONCEPT	`recursion (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP189

All clusters are made of objects of the same texture vs. not all clusters are made of objects of the same texture.

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	CROSSREFS	`Adjacent-numbered pages: BP184 BP185 BP186 BP187 BP188 * BP190 BP191 BP192 BP193 BP194`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_feature (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP101

Parallel dents vs. perpendicular dents.

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	CROSSREFS	`Adjacent-numbered pages: BP96 BP97 BP98 BP99 BP100 * BP102 BP103 BP104 BP105 BP106`
	KEYWORD	`traditional`
	CONCEPT	`indentation (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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`

BP1

Empty image vs. non-empty image.

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	COMMENTS	`The first Bongard Problem.` `All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: * BP2 BP3 BP4 BP5 BP6`
	EXAMPLE	`A circle fits on the right because it is not nothing.`
	KEYWORD	`easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `zero (info \| search)`
	WORLD	`zoom in left (blank_image) \| zoom in right (curves_drawing)`
	AUTHOR	`Mikhail M. Bongard`

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