The On-Line Encyclopedia of Bongard Problems

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Shapes have equal area vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP930 BP931 BP932 BP933 BP934 * BP936 BP937 BP938 BP939 BP940`
	KEYWORD	`nice, precise, allsorted, unstable, left-narrow, perfect, pixelperfect, unorderedpair`
	CONCEPT	`area (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP937

Shapes have equal perimeter vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP932 BP933 BP934 BP935 BP936 * BP938 BP939 BP940 BP941 BP942`
	KEYWORD	`precise, allsorted, unstable, left-narrow, perfect, unorderedpair`
	CONCEPT	`perimeter (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP949

Two unique distances between points vs. three unique distances between points.

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

	CROSSREFS	`Adjacent-numbered pages: BP944 BP945 BP946 BP947 BP948 * BP950 BP951 BP952 BP953 BP954`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, traditional, preciseworld`
	CONCEPT	`two (info \| search),` `three (info \| search)`
	WORLD	`3_or_4_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP953

Image of this Bongard Problem vs. empty image.

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	COMMENTS	`"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes.`
	CROSSREFS	`See BP959, BP902.` `Adjacent-numbered pages: BP948 BP949 BP950 BP951 BP952 * BP954 BP955 BP956 BP957 BP958`
	KEYWORD	`nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`zoom in left (bp953_image) \| zoom in right (blank_image)`
	AUTHOR	`Leo Crabbe`

BP959

This image of this Bongard Problem vs. empty image.

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	CROSSREFS	`See BP953, BP902.` `Adjacent-numbered pages: BP954 BP955 BP956 BP957 BP958 * BP960 BP961 BP962 BP963 BP964`
	KEYWORD	`meta (see left/right), miniproblems, left-finite, right-finite, left-full, right-full, right-null, perfect, infinitedetail, finished, experimental, funny`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`zoom in left \| zoom in right (blank_image)`
	AUTHOR	`Aaron David Fairbanks, Leo Crabbe`

BP961

Includes itself on the left vs. includes itself on the right.

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	COMMENTS	`Some examples are Bongard Problems with this solution.`
	CROSSREFS	`Adjacent-numbered pages: BP956 BP957 BP958 BP959 BP960 * BP962 BP963 BP964 BP965 BP966`
	KEYWORD	`nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP965

If you place the image on top of itself so that it lines up with itself exactly within a small region, it also lines up everywhere else vs. not so.

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	COMMENTS	`Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.` `Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.`
	CROSSREFS	`See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.` `Adjacent-numbered pages: BP960 BP961 BP962 BP963 BP964 * BP966 BP967 BP968 BP969 BP970`
	KEYWORD	`hard, precise, distractingworld, perfect`
	CONCEPT	`local_global (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP966

Even number of white regions vs. odd number of white regions.

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	COMMENTS	`See BP889 for the version in which the background doesn't count.`
	CROSSREFS	`Adjacent-numbered pages: BP961 BP962 BP963 BP964 BP965 * BP967 BP968 BP969 BP970 BP971`
	KEYWORD	`nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP990

The center of mass can "see" (in straight lines) all points within the shape vs. the center of mass is not located in a region where it can see (in straight lines) all points.

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	COMMENTS	`Another way of thinking about the solution is considering whether a light source placed at the center of mass of a given example would illuminate the whole shape.`
	CROSSREFS	`Every left for this Problem would be will be a left example for both BP367 and BP368.` `Adjacent-numbered pages: BP985 BP986 BP987 BP988 BP989 * BP991 BP992 BP993 BP994 BP995`
	KEYWORD	`convoluted, perfect`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_seeing_point_center_of_mass_inside [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP991

Can be arranged with multiple copies of itself to form some convex shape vs. not so.

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

	CROSSREFS	`This is a generalization of BP820.` `Adjacent-numbered pages: BP986 BP987 BP988 BP989 BP990 * BP992 BP993 BP994 BP995 BP996`
	KEYWORD	`precise, allsorted, perfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

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