The On-Line Encyclopedia of Bongard Problems

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BP70

There are no side branches of the second order vs. there are side branches of the second order.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.`
	CROSSREFS	`Adjacent-numbered pages: BP65 BP66 BP67 BP68 BP69 * BP71 BP72 BP73 BP74 BP75`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`recursion_number (info \| search),` `recursion (info \| search),` `tracing_line_or_curve (info \| search),` `trunk_of_tree (info \| search),` `two (info \| search)`
	WORLD	`curve_tree [smaller \| same \| bigger] zoom in left (curve_tree_one_level)`
	AUTHOR	`Mikhail M. Bongard`

BP71

There are inside figures of the second order vs. there are no inside figures of the second order.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.`
	CROSSREFS	`See BP1022 for a Problem about presence of nesting.` `Adjacent-numbered pages: BP66 BP67 BP68 BP69 BP70 * BP72 BP73 BP74 BP75 BP76`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`recursion_number (info \| search),` `inside (info \| search),` `recursion (info \| search),` `two (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP167

Every cluster has two clusters of dots vs. every cluster has three clusters of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP162 BP163 BP164 BP165 BP166 * BP168 BP169 BP170 BP171 BP172`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `recursion (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP186

Object made of objects vs. object made of objects made of objects.

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

	CROSSREFS	`Adjacent-numbered pages: BP181 BP182 BP183 BP184 BP185 * BP187 BP188 BP189 BP190 BP191`
	KEYWORD	`traditional`
	CONCEPT	`recursion (info \| search),` `cluster (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP188

Shape of whole different from shape of parts vs. shape of whole same as shape of parts.

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	CROSSREFS	`See BP1002 for more general visual self-similarity.` `See BP1064 for a similar Problem about two shapes inter-referencing instead of just one shape referencing itself.` `Adjacent-numbered pages: BP183 BP184 BP185 BP186 BP187 * BP189 BP190 BP191 BP192 BP193`
	KEYWORD	`traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP322

One outer outline vs. more than one outer outline.

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

	CROSSREFS	`Adjacent-numbered pages: BP317 BP318 BP319 BP320 BP321 * BP323 BP324 BP325 BP326 BP327`
	KEYWORD	`nice, precise, allsorted, traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `outer_outline (info \| search),` `recursion (info \| search),` `one (info \| search)`
	WORLD	`nest_shapes [smaller \| same \| bigger]`
	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`

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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	COMMENTS	`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.`
	CROSSREFS	`Adjacent-numbered pages: BP528 BP529 BP530 BP531 BP532 * BP534 BP535 BP536 BP537 BP538`
	KEYWORD	`nice, 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`

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