The On-Line Encyclopedia of Bongard Problems

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BP344

Shape can tile itself vs. shape cannot tile itself.

(edit; present; nest [left/right]; search; history)

	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`

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	`precise, unstable, physics, 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	`See BP388 for whether a distinguished point can see all points.` `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`

BP523

Same amount of black in any vertical slice vs. varying amounts of black in vertical slices.

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	CROSSREFS	`Adjacent-numbered pages: BP518 BP519 BP520 BP521 BP522 * BP524 BP525 BP526 BP527 BP528`
	KEYWORD	`nice, precise, rotate, stretch, unstable, perfect, pixelperfect, traditional`
	WORLD	`shapes_can_touch_box [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP541

Bongard Problems vs. anything else.

BP1

BP2

BP3

BP4

BP541

BP1073

blllmam

cat

nongard

(edit; present; nest [left/right]; search; history)

	COMMENTS	`This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.`
	CROSSREFS	`Adjacent-numbered pages: BP536 BP537 BP538 BP539 BP540 * BP542 BP543 BP544 BP545 BP546`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bp)`
	AUTHOR	`Aaron David Fairbanks`

BP542

BP Pages on the OEBP vs. anything else.

BP1

BP2

BP3

BP542

BP1073

BP0

nolab

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP537 BP538 BP539 BP540 BP541 * BP543 BP544 BP545 BP546 BP547`
	KEYWORD	`notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bppage)`
	AUTHOR	`Aaron David Fairbanks`

BP544

Everything vs. nothing.

	&(%	0	BP1	BP544	BP1073
		dog	nothing

(edit; present; nest [left/right]; search; history)

	COMMENTS	`All ideas and things, with no limits.`
	CROSSREFS	`Adjacent-numbered pages: BP539 BP540 BP541 BP542 BP543 * BP545 BP546 BP547 BP548 BP549`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny`
	CONCEPT	`existence (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (everything) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

BP559

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

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	COMMENTS	`All examples 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, 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`

BP570

Shape outlines that aren't triangles vs. black shapes that aren't squares.

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	COMMENTS	`An example of an overriddensolution.`
	CROSSREFS	`Adjacent-numbered pages: BP565 BP566 BP567 BP568 BP569 * BP571 BP572 BP573 BP574 BP575`
	KEYWORD	`less, example, overriddensolution, experimental, funny, neither`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP816

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

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP811 BP812 BP813 BP814 BP815 * BP817 BP818 BP819 BP820 BP821`
	KEYWORD	`precise, notso, stretch, unstable, perfect`
	CONCEPT	`cross_section (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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