The On-Line Encyclopedia of Bongard Problems

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A large hole vs. a small hole.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP29 BP30 BP31 BP32 BP33 * BP35 BP36 BP37 BP38 BP39`
	KEYWORD	`spectrum, stable, finished, traditional, bongard`
	CONCEPT	`hole (info \| search),` `size (info \| search),` `texture (info \| search)`
	WORLD	`shape_one_hole [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

The axis of the hole is parallel to the figure axis vs. the axis of the hole is perpendicular to the figure axis.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP30 BP31 BP32 BP33 BP34 * BP36 BP37 BP38 BP39 BP40`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`hole (info \| search),` `line_slope (info \| search),` `same (info \| search),` `texture (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	WORLD	`elongated_shape_one_small_elongated_centered_hole [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Two of the shapes make tiles along their border lines vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP196 BP197 BP198 BP199 BP200 * BP202 BP203 BP204 BP205 BP206`
	KEYWORD	`noisy, traditional`
	CONCEPT	`rotation_required (info \| search),` `tiling (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Giuseppe Insana`

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`

High approximate similarity vs. lower approximate similarity.

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	CROSSREFS	`Adjacent-numbered pages: BP333 BP334 BP335 BP336 BP337 * BP339 BP340 BP341 BP342 BP343`
	KEYWORD	`spectrum, traditional, continuous`
	CONCEPT	`imperfection_small (info \| search),` `same_shape (info \| search),` `same (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	WORLD	`two_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No two shapes are the same vs. at least two shapes are the same.

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	CROSSREFS	`BP57 is the same solution except all examples have two shapes.` `Adjacent-numbered pages: BP338 BP339 BP340 BP341 BP342 * BP344 BP345 BP346 BP347 BP348`
	KEYWORD	`traditional, collection`
	CONCEPT	`existence (info \| search),` `identical (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search)`
	WORLD	`shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Shape can tile itself vs. shape cannot tile itself.

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	COMMENTS	`Left examples are sometimes called "rep-tiles."` `The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.` `Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."`
	CROSSREFS	`See BP532 for a version with fractals.` `Adjacent-numbered pages: BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349`
	EXAMPLE	`Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.`
	KEYWORD	`hard, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Intersection of circle and square vs. union of circle and square.

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	COMMENTS	`An image of only a circle or of only a square would be ambiguously categorized.`
	CROSSREFS	`Adjacent-numbered pages: BP340 BP341 BP342 BP343 BP344 * BP346 BP347 BP348 BP349 BP350`
	KEYWORD	`nice, left-narrow, right-narrow, traditional, both`
	CONCEPT	`set_intersection (info \| search),` `set_union (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Shape on the right is the convex hull of shape on the left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP343 BP344 BP345 BP346 BP347 * BP349 BP350 BP351 BP352 BP353`
	KEYWORD	`precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Center of mass within the black area of the shape vs. center of mass out of the black area of the shape.

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	CROSSREFS	`Adjacent-numbered pages: BP362 BP363 BP364 BP365 BP366 * BP368 BP369 BP370 BP371 BP372`
	KEYWORD	`precise, unstable, physics, perfect, pixelperfect, traditional`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (shape_center_of_mass_falls_inside)`
	AUTHOR	`Aaron David Fairbanks`

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