The On-Line Encyclopedia of Bongard Problems

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Fractal tiles itself with uniformly scaled-down copies of itself vs. fractal tiles itself with stretched copies of itself.

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	COMMENTS	`"Self-similar" vs. "self-affine."`
	CROSSREFS	`Adjacent-numbered pages: BP525 BP526 BP527 BP528 BP529 * BP531 BP532 BP533 BP534 BP535`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`fractal_self_tile_affine_allowed [smaller \| same \| bigger] zoom in left (fractal_self_tile)`
	AUTHOR	`Aaron David Fairbanks`

BP531

Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself.

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	COMMENTS	`More specifically, all left examples shown in this Problem have Hausdorff dimension log2(3) while all right examples have Hausdorff dimension log3(5).` `Left examples can tile themselves by any power of 3 smaller same-sized copies of themselves while right examples can tile themselves by any power of 5 smaller same-sized copies of themselves.` `Homage to Bongard's original three versus five Problems.`
	CROSSREFS	`Adjacent-numbered pages: BP526 BP527 BP528 BP529 BP530 * BP532 BP533 BP534 BP535 BP536`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `three (info \| search),` `five (info \| search)`
	WORLD	`fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP532

Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself.

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	CROSSREFS	`This is BP344 ("rep-tiles") but for fractals.` `See BP1119 for the version with multiple different sizes of tile allowed.` `Adjacent-numbered pages: BP527 BP528 BP529 BP530 BP531 * BP533 BP534 BP535 BP536 BP537`
	KEYWORD	`hardsort, proofsrequired, perfect, infinitedetail, contributepairs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left (fractal_self_tile)`
	AUTHOR	`Aaron David Fairbanks`

BP533

Contains smaller copy of itself vs. doesn't.

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	CROSSREFS	`Adjacent-numbered pages: BP528 BP529 BP530 BP531 BP532 * BP534 BP535 BP536 BP537 BP538`
	EXAMPLE	`A smaller copy of EX6409 (the black area) can be located within itself, but some of the white space inside it is not retained in this smaller copy.`
	KEYWORD	`perfect, infinitedetail, contributepairs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_built_from_self_tile_fractals [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP536

All gears can make complete turns vs. not so.

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	CROSSREFS	`See BP336 for one gear turns all.` `Adjacent-numbered pages: BP531 BP532 BP533 BP534 BP535 * BP537 BP538 BP539 BP540 BP541`
	KEYWORD	`stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `gear (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP538

Shown is a box of this Bongard Problem (BP538) vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP533 BP534 BP535 BP536 BP537 * BP539 BP540 BP541 BP542 BP543`
	KEYWORD	`less, notso, left-finite, finished, invalid, experimental, funny`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP540

Objects define a map from the top row of boxes to the bottom row of boxes vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Map_(mathematics)`
	CROSSREFS	`Adjacent-numbered pages: BP535 BP536 BP537 BP538 BP539 * BP541 BP542 BP543 BP544 BP545`
	AUTHOR	`Jago Collins`

BP543

Image depicting infinitely many objects vs. image depicting finitely many objects.

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	COMMENTS	`Another solution is "evokes infinity vs. not so." Or "seen as having arbitrarily fine detail." All left examples show objects getting smaller and smaller and closer and closer together approaching some limit within the box.`
	CROSSREFS	`Adjacent-numbered pages: BP538 BP539 BP540 BP541 BP542 * BP544 BP545 BP546 BP547 BP548`
	KEYWORD	`nice, abstract, concept, infinitedetail`
	CONCEPT	`finite_infinite (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP545

Solution for this problem (BP545) in English text vs. not.

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	COMMENTS	`This Problem admits multiple solutions besides "Solution for this problem in English text vs. not so," some of which are listed as the left examples. Some do not depend on the English language, so this Problem is technically "solvable" without the relevant cultural information.`
	CROSSREFS	`Adjacent-numbered pages: BP540 BP541 BP542 BP543 BP544 * BP546 BP547 BP548 BP549 BP550`
	KEYWORD	`less, notso, culture, finished, invalid, experimental, funny`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP548

Due to pixelation, it is ambiguous whether the middle small shape is a resized version of the left shape or the right shape vs. there is a clear choice.

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	COMMENTS	`A strange Problem relying on pixelation of digital images.`
	CROSSREFS	`Adjacent-numbered pages: BP543 BP544 BP545 BP546 BP547 * BP549 BP550 BP551 BP552 BP553`
	KEYWORD	`less, creativeexamples, pixelperfect, structure, orderedtriplet, experimental`
	CONCEPT	`imperfection_small (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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