The On-Line Encyclopedia of Bongard Problems

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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, 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`

BP346

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`

BP350

Some quantity keeps increasing from left to right vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP345 BP346 BP347 BP348 BP349 * BP351 BP352 BP353 BP354 BP355`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`quantity_vary_seq_noise_allowed [smaller \| same \| bigger] zoom in left (quantity_change_seq_increase_right_noise_allowed)`
	AUTHOR	`Aaron David Fairbanks`

BP351

Discrete quantity vs. continuous quantity.

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	CROSSREFS	`See BP873 for the version with Bongard Problems.` `Adjacent-numbered pages: BP346 BP347 BP348 BP349 BP350 * BP352 BP353 BP354 BP355 BP356`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `discrete_continuous (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in left (constant_change_discrete_seq_increase_right)`
	AUTHOR	`Aaron David Fairbanks`

BP352

Increasing quantity has no lower (or upper) bound (and gives a representation of negative numbers) vs. increasing quantity has lower (and/or upper) bound.

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	COMMENTS	`All left examples have a clear "zero" value, but it may be unclear which side is meant to be positive and which side is meant to be negative (See BP893^left for quantities without clear notion of increase/decrease.)`
	CROSSREFS	`See BP353^left for looping quantities; these do not clearly represent positive and negative numbers, but they can likewise unboundedly decrease and increase.` `Adjacent-numbered pages: BP347 BP348 BP349 BP350 BP351 * BP353 BP354 BP355 BP356 BP357`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in right (constant_change_seq_increase_right_lower_bound)`
	AUTHOR	`Aaron David Fairbanks`

BP353

Increasing quantity loops back to starting value vs. increasing quantity cannot loop back to starting value.

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	CROSSREFS	`Adjacent-numbered pages: BP348 BP349 BP350 BP351 BP352 * BP354 BP355 BP356 BP357 BP358`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules, miniworlds`
	CONCEPT	`iteration (info \| search),` `loop (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in left (constant_change_seq_loop_right)`
	AUTHOR	`Aaron David Fairbanks`

BP354

Increasing quantity is angular vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP349 BP350 BP351 BP352 BP353 * BP355 BP356 BP357 BP358 BP359`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules, miniworlds`
	CONCEPT	`angle (info \| search),` `loop (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP355

Fractal iteration based on 2-D (shapes) vs. fractal iteration based on 1-D (line segments).

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	CROSSREFS	`Adjacent-numbered pages: BP350 BP351 BP352 BP353 BP354 * BP356 BP357 BP358 BP359 BP360`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`fractal (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_fractal_iterate_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP356

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`

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