The On-Line Encyclopedia of Bongard Problems

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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`

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`

Object on the right fits in pattern on the left vs. object on the right does not fit in pattern on the left.

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	CROSSREFS	`Adjacent-numbered pages: BP341 BP342 BP343 BP344 BP345 * BP347 BP348 BP349 BP350 BP351`
	KEYWORD	`nice, creativeexamples, structure, traditional, rules`
	CONCEPT	`categorization (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

No pattern (variety of shapes) vs. all shapes have something in common.

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	CROSSREFS	`See BP378 for a similar idea using just two objects per example.` `Adjacent-numbered pages: BP342 BP343 BP344 BP345 BP346 * BP348 BP349 BP350 BP351 BP352`
	KEYWORD	`nice, left-unknowable, right-narrow, traditional`
	CONCEPT	`existence (info \| search),` `shape_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search)`
	WORLD	`several_small_misc [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	`nice, precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Object at lower-right fits as n-th item in the top row of objects, where n is the number of dots at lower-left vs. not so.

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	COMMENTS	`All examples have a number of dots in the bottom left corner, an object in the bottom right corner, and a sequence of object at the top.`
	CROSSREFS	`Adjacent-numbered pages: BP351 BP352 BP353 BP354 BP355 * BP357 BP358 BP359 BP360 BP361`
	KEYWORD	`nice, creativeexamples, left-narrow, structure, traditional, rules, miniworlds`
	CONCEPT	`fractal (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search),` `feature_cluster (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

The circles will collide if the arrows are their velocities vs. the circles will not collide if the arrows are their velocities.

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	CROSSREFS	`Adjacent-numbered pages: BP353 BP354 BP355 BP356 BP357 * BP359 BP360 BP361 BP362 BP363`
	KEYWORD	`nice, physics, unorderedpair, traditional`
	CONCEPT	`arrow (info \| search),` `tracing_lines_or_curves_meet (info \| search),` `speed (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `imagined_motion (info \| search),` `motion (info \| search),` `collision (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Random arrangement of pixels vs. not so.

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	COMMENTS	`By "random" we mean it's reasonable to expect each pixel in the image was chosen with a constant, consistent chance of being black or white.`
	CROSSREFS	`Adjacent-numbered pages: BP354 BP355 BP356 BP357 BP358 * BP360 BP361 BP362 BP363 BP364`
	KEYWORD	`nice, right-narrow, collective, experimental, blackwhiteinvariant`
	CONCEPT	`pattern_or_random (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Order is high (low entropy) vs. order is low (high entropy).

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	COMMENTS	`"Order versus chaos."`
	CROSSREFS	`Adjacent-numbered pages: BP355 BP356 BP357 BP358 BP359 * BP361 BP362 BP363 BP364 BP365`
	KEYWORD	`nice, abstract, collective, contributepairs, traditional, miniworlds`
	CONCEPT	`pattern_or_random (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Counterclockwise along the curve following the arrow vs. clockwise along the curve following the arrow.

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	CROSSREFS	`Adjacent-numbered pages: BP358 BP359 BP360 BP361 BP362 * BP364 BP365 BP366 BP367 BP368`
	KEYWORD	`easy, nice, dual, handed, leftright, updown, gap, traditional`
	CONCEPT	`arrow (info \| search),` `turn_orientation (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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