The On-Line Encyclopedia of Bongard Problems

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BP122

Line divides interior into two regions vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP117 BP118 BP119 BP120 BP121 * BP123 BP124 BP125 BP126 BP127`
	KEYWORD	`traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `number (info \| search),` `tiling (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP201

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`

BP229

When the objects are rotated and their dots are overlapped and eliminated, they form three-square-tall structures with columns of the same color vs. not so.

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	COMMENTS	`Explanation / justification of BP229 by its creator:` `"Long (doubly sized) objects are purines (A & G).` `Short objects are pyrimidines (C & T).` `Black are those forming triple Hbond (G and C).` `White are those forming double Hbond (A & T).` `On the left we have matching codes, i.e., bases, doublets or triplets that, when rotated, can pair correctly (A with T, G with C), binding the two strands.` `On the right we have objects that no matter how they are rotated they do not pair correctly (because of bumps, wrong color codes, etc)."`
	CROSSREFS	`Adjacent-numbered pages: BP224 BP225 BP226 BP227 BP228 * BP230 BP231 BP232 BP233 BP234`
	KEYWORD	`unorderedpair, traditional`
	CONCEPT	`rotation_required (info \| search),` `tiling (info \| search),` `specific_value (info \| search),` `specificity (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP283

Rectangle left after tiling all black shapes into empty square vs. triangle left after tiling all black shapes into empty square.

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	CROSSREFS	`Adjacent-numbered pages: BP278 BP279 BP280 BP281 BP282 * BP284 BP285 BP286 BP287 BP288`
	KEYWORD	`traditional`
	CONCEPT	`outlined_filled (info \| search),` `tiling (info \| search),` `texture (info \| search),` `triangle (info \| search)`
	AUTHOR	`Sang-Joon Yoon`

BP289

Shapes, if tiled up properly, form a square vs. shapes cannot form a square no matter how they are tiled.

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	CROSSREFS	`Adjacent-numbered pages: BP284 BP285 BP286 BP287 BP288 * BP290 BP291 BP292 BP293 BP294`
	KEYWORD	`nice, stretch, traditional`
	CONCEPT	`square (info \| search),` `tiling (info \| search)`
	AUTHOR	`"Lewis"`

BP323

Jigsaw puzzle pieces can be assembled into a square vs. jigsaw puzzle pieces cannot be assembled into a square.

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	COMMENTS	`Although it takes time to check each individual example, the right answer is likely the first thing a person would think of upon seeing this.`
	CROSSREFS	`Adjacent-numbered pages: BP318 BP319 BP320 BP321 BP322 * BP324 BP325 BP326 BP327 BP328`
	KEYWORD	`notso, hardsort, traditional`
	CONCEPT	`jigsaw_puzzle (info \| search),` `tiling (info \| search),` `imagined_motion (info \| search),` `motion (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`

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`

BP386

Lower shape can be used as a tile to build the upper one vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP381 BP382 BP383 BP384 BP385 * BP387 BP388 BP389 BP390 BP391`
	KEYWORD	`nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable`
	CONCEPT	`tiling (info \| search)`
	AUTHOR	`Jago Collins`

BP529

Fractal tiles itself with smaller non-rotated (nor reflected) copies of itself vs. fractal requires turning to tile itself.

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	COMMENTS	`No included examples involve reflection.`
	CROSSREFS	`Adjacent-numbered pages: BP524 BP525 BP526 BP527 BP528 * BP530 BP531 BP532 BP533 BP534`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `rotation_required (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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