The On-Line Encyclopedia of Bongard Problems

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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`

BP31

One line vs. two lines.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP26 BP27 BP28 BP29 BP30 * BP32 BP33 BP34 BP35 BP36`
	KEYWORD	`easy, precise, allsorted, left-narrow, right-narrow, pixelperfect, traditional, bongard`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `one (info \| search),` `two (info \| search)`
	WORLD	`smooth_crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP210

Part of at least one object is out of box vs. all objects are within the box.

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	COMMENTS	`Alternatively, "black touches the boundary vs. not".`
	CROSSREFS	`Adjacent-numbered pages: BP205 BP206 BP207 BP208 BP209 * BP211 BP212 BP213 BP214 BP215`
	KEYWORD	`precise, boundingbox, perfect, pixelperfect, traditional`
	CONCEPT	`completed_out_of_box (info \| search),` `existence (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP211

More black than white vs. more white than black.

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	CROSSREFS	`See BP196 for a version of this Problem restricted to uniform textures.` `Adjacent-numbered pages: BP206 BP207 BP208 BP209 BP210 * BP212 BP213 BP214 BP215 BP216`
	KEYWORD	`easy, nice, spectrum, dual, blackwhite, unstable, right-null, perfect, pixelperfect, traditional, continuous, viceversa, bordercontent`
	CONCEPT	`outlined_filled (info \| search),` `size (info \| search),` `texture (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Giuseppe Insana`

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`

BP279

The left part has more pixels (area) than the right part vs. the left part has fewer pixels than the right part.

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	CROSSREFS	`Adjacent-numbered pages: BP274 BP275 BP276 BP277 BP278 * BP280 BP281 BP282 BP283 BP284`
	KEYWORD	`dual, handed, leftright, pixelperfect`
	CONCEPT	`left_right (info \| search),` `length_line_or_curve (info \| search),` `area (info \| search)`
	WORLD	`arial_font_two_symbols [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP321

Small round object unreachable from the border of the box vs. small round object reachable from the border of the box.

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	COMMENTS	`Equivalently, "small round object enclosed by white loop vs. not so."`
	CROSSREFS	`Adjacent-numbered pages: BP316 BP317 BP318 BP319 BP320 * BP322 BP323 BP324 BP325 BP326`
	KEYWORD	`nice, precise, allsorted, boundingbox, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`bounding_box (info \| search),` `path (info \| search),` `reachable (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP324

Left shapes can be placed on top of each other to make right shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP319 BP320 BP321 BP322 BP323 * BP325 BP326 BP327 BP328 BP329`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`set_union (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP325

Left shapes can combine by symmetric difference (XOR logical operator) to make right shape vs. left shapes can combine by intersection (AND logical operator) to make right shape.

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	CROSSREFS	`Adjacent-numbered pages: BP320 BP321 BP322 BP323 BP324 * BP326 BP327 BP328 BP329 BP330`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`xor (info \| search),` `overlap (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP335

Tessellates the plane vs. does not tessellate the plane.

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	COMMENTS	`EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021`
	CROSSREFS	`Adjacent-numbered pages: BP330 BP331 BP332 BP333 BP334 * BP336 BP337 BP338 BP339 BP340`
	KEYWORD	`nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape)`
	AUTHOR	`Aaron David Fairbanks`

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