The On-Line Encyclopedia of Bongard Problems

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BP34

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`

BP35

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`

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`

BP344

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, nice, 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`

BP345

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`

BP367

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	`nice, precise, unstable, 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`

BP368

There is a point that can see (in straight lines) all points vs. there is no point that can see (in straight lines) all points.

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	COMMENTS	`Left examples are called "star domains."`
	CROSSREFS	`Adjacent-numbered pages: BP363 BP364 BP365 BP366 BP367 * BP369 BP370 BP371 BP372 BP373`
	KEYWORD	`nice, precise, unstable, perfect, traditional`
	CONCEPT	`all (info \| search),` `existence (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape_with_seeing_point)`
	AUTHOR	`Aaron David Fairbanks`

BP559

Cross section of a cube vs. not cross section of a cube

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	COMMENTS	`All examples in this Problem are solid black shapes.` `This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020`
	CROSSREFS	`Adjacent-numbered pages: BP554 BP555 BP556 BP557 BP558 * BP560 BP561 BP562 BP563 BP564`
	KEYWORD	`hard, nice, precise, allsorted, notso, stretch, challenge, left-narrow, perfect`
	CONCEPT	`cube (info \| search),` `cross_section (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP820

Shape can be combined with a copy of itself to form a convex shape vs. not so.

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	CROSSREFS	`For the generalization of this property, see BP991.` `Adjacent-numbered pages: BP815 BP816 BP817 BP818 BP819 * BP821 BP822 BP823 BP824 BP825`
	KEYWORD	`nice, precise, allsorted`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Isaac Hathaway`

BP854

Nothing vs. nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP849 BP850 BP851 BP852 BP853 * BP855 BP856 BP857 BP858 BP859`
	KEYWORD	`left-finite, right-finite, left-full, right-full, finished, experimental, funny`
	WORLD	`nothing [same \| bigger] zoom in left (nothing) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

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