The On-Line Encyclopedia of Bongard Problems

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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`

Small shape present vs. all shapes large.

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	COMMENTS	`All examples in this problem include three or fewer outlines of circles and (non-skinny) triangles.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.`
	CROSSREFS	`Adjacent-numbered pages: BP16 BP17 BP18 BP19 BP20 * BP22 BP23 BP24 BP25 BP26`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`existence (info \| search),` `size (info \| search)`
	WORLD	`circle_triangle_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

A circle vs. no 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. 221.`
	CROSSREFS	`Adjacent-numbered pages: BP19 BP20 BP21 BP22 BP23 * BP25 BP26 BP27 BP28 BP29`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`circle (info \| search),` `existence (info \| search)`
	WORLD	`circle_square_eq-tri_small_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Solid black triangle vs. no solid black triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.`
	CROSSREFS	`Adjacent-numbered pages: BP21 BP22 BP23 BP24 BP25 * BP27 BP28 BP29 BP30 BP31`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`and (info \| search),` `existence (info \| search),` `outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `texture (info \| search),` `triangle (info \| search)`
	WORLD	`circle_eq-tri_small_some_outline_some_fill [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

A curve with one self-crossing vs. a curve without a self-crossing.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.`
	CROSSREFS	`BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.` `Adjacent-numbered pages: BP25 BP26 BP27 BP28 BP29 * BP31 BP32 BP33 BP34 BP35`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`x-crossing (info \| search),` `existence (info \| search)`
	WORLD	`crosscurve [smaller \| same \| bigger] zoom in right (curve_or_outline)`
	AUTHOR	`Mikhail M. Bongard`

Acute angle vs. no acute angle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP28 BP29 BP30 BP31 BP32 * BP34 BP35 BP36 BP37 BP38`
	KEYWORD	`nice, stretch, finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `existence (info \| search)`
	WORLD	`Multiple options: mediumsize_centered_outline [smaller \| same \| bigger], shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

The chain does not branch vs. the chain branches.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`Adjacent-numbered pages: BP87 BP88 BP89 BP90 BP91 * BP93 BP94 BP95 BP96 BP97`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`all (info \| search),` `branch_point (info \| search),` `collinear (info \| search),` `existence (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

No cycle vs. a cycle exists.

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	CROSSREFS	`Adjacent-numbered pages: BP113 BP114 BP115 BP116 BP117 * BP119 BP120 BP121 BP122 BP123`
	KEYWORD	`traditional`
	CONCEPT	`arrow (info \| search),` `cyclic_path (info \| search),` `existence (info \| search),` `path (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

A small correction will result in a single circle vs. no small correction will result in a single circle.

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	CROSSREFS	`Adjacent-numbered pages: BP114 BP115 BP116 BP117 BP118 * BP120 BP121 BP122 BP123 BP124`
	KEYWORD	`fuzzy, traditional`
	CONCEPT	`existence (info \| search),` `imperfection_small (info \| search)`
	WORLD	`curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

Dots are vertices of a parallelogram vs. dots are not vertices of a parallelogram.

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	CROSSREFS	`Adjacent-numbered pages: BP126 BP127 BP128 BP129 BP130 * BP132 BP133 BP134 BP135 BP136`
	KEYWORD	`noisy, traditional`
	CONCEPT	`existence (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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