The On-Line Encyclopedia of Bongard Problems

Search: author:Aaron David Fairbanks

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Shape on the right is the convex hull of shape on the left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP343 BP344 BP345 BP346 BP347 * BP349 BP350 BP351 BP352 BP353`
	KEYWORD	`precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No pattern (variety of shapes) vs. all shapes have something in common.

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	CROSSREFS	`See BP378 for a similar idea using just two objects per example.` `Adjacent-numbered pages: BP342 BP343 BP344 BP345 BP346 * BP348 BP349 BP350 BP351 BP352`
	KEYWORD	`nice, left-unknowable, right-narrow, traditional, collection`
	CONCEPT	`existence (info \| search),` `shape_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search)`
	WORLD	`several_small_misc [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Object on the right fits in pattern on the left vs. object on the right does not fit in pattern on the left.

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

	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`

Intersection of circle and square vs. union of circle and square.

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	COMMENTS	`An image of only a circle or of only a square would be ambiguously categorized.`
	CROSSREFS	`Adjacent-numbered pages: BP340 BP341 BP342 BP343 BP344 * BP346 BP347 BP348 BP349 BP350`
	KEYWORD	`nice, left-narrow, right-narrow, traditional, both`
	CONCEPT	`set_intersection (info \| search),` `set_union (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

No two shapes are the same vs. at least two shapes are the same.

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

	CROSSREFS	`BP57 is the same solution except all examples have two shapes.` `Adjacent-numbered pages: BP338 BP339 BP340 BP341 BP342 * BP344 BP345 BP346 BP347 BP348`
	KEYWORD	`traditional, collection`
	CONCEPT	`existence (info \| search),` `identical (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search)`
	WORLD	`shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Exactly one axis of symmetry vs. either zero or more than one axis of symmetry.

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

	CROSSREFS	`Adjacent-numbered pages: BP337 BP338 BP339 BP340 BP341 * BP343 BP344 BP345 BP346 BP347`
	KEYWORD	`traditional, finishedexamples`
	CONCEPT	`exists_one (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Strictly increasing or strictly decreasing border line vs. both increasing and decreasing border line.

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

	CROSSREFS	`Adjacent-numbered pages: BP336 BP337 BP338 BP339 BP340 * BP342 BP343 BP344 BP345 BP346`
	KEYWORD	`math, perfect, pixelperfect, traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `or (info \| search),` `outlined_filled (info \| search),` `tracing_line_or_curve (info \| search),` `texture (info \| search)`
	WORLD	`function_graph_black_below_white_above [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Regular star polygon vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP335 BP336 BP337 BP338 BP339 * BP341 BP342 BP343 BP344 BP345`
	KEYWORD	`math, traditional`
	CONCEPT	`tracing_line_or_curve (info \| search),` `vertex_of_meeting_lines (info \| search),` `write_in_single_stroke (info \| search)`
	WORLD	`figure_made_of_segments [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Union of left sets is right set vs. intersection of left sets is right set.

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	CROSSREFS	`Adjacent-numbered pages: BP334 BP335 BP336 BP337 BP338 * BP340 BP341 BP342 BP343 BP344`
	KEYWORD	`math, structure, orderedtriplet, traditional, both, neither`
	CONCEPT	`set_intersection (info \| search),` `left_right (info \| search),` `set_union (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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