The On-Line Encyclopedia of Bongard Problems

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BP528

Highly iterated fractal vs. fractal after only few iterations.

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	CROSSREFS	`Adjacent-numbered pages: BP523 BP524 BP525 BP526 BP527 * BP529 BP530 BP531 BP532 BP533`
	KEYWORD	`world, contributepairs`
	CONCEPT	`fractal (info \| search)`
	WORLD	`zoom in left (fractal)`
	AUTHOR	`Aaron David Fairbanks`

BP529

Fractal tiles itself with smaller non-rotated (nor reflected) copies of itself vs. fractal requires turning to tile itself.

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	COMMENTS	`No included examples involve reflection.`
	CROSSREFS	`Adjacent-numbered pages: BP524 BP525 BP526 BP527 BP528 * BP530 BP531 BP532 BP533 BP534`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `rotation_required (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP530

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`

BP534

Bongard Problems such that potential left examples can intuitively be put in bijection with potential right examples vs. other Bongard Problems.

BP7	BP8	BP19	BP36	BP43	BP45
BP54	BP55	BP63	BP64	BP67	BP95
BP106	BP109	BP157	BP158	BP180	BP196
BP197	BP211	BP234	BP278	BP279	BP286
BP313	BP337	BP357	BP363	BP372	BP513
BP514	BP515	BP516	BP517	BP793	. . .

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	COMMENTS	`This is the keyword "dual" on the OEBP.` `Given an example there is some way to "flip sides" by altering it. The left-to-right and right-to-left transformations should be inverses.` `It is not required that there only be one such transformation. For example, for many handed Bongard Problem, flipping an example over any axis will reliably switch its sorting.` `It is not required that every left example must have its corresponding right example uploaded on the OEBP nor vice versa. See the keyword contributepairs for the BPs the OEBP advises users upload left and right examples for in pairs.`
	CROSSREFS	`Adjacent-numbered pages: BP529 BP530 BP531 BP532 BP533 * BP535 BP536 BP537 BP538 BP539`
	KEYWORD	`meta (see left/right), links, keyword, sideless`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP535

Visual Bongard Problems such that flipping over the vertical axis (left/right) can switch an example's side vs. visual Bongard Problems whose examples' sorting doesn't change under such a transformation.

BP8	BP43	BP67	BP109	BP207	BP234
BP278	BP279	BP313	BP337	BP357	BP363
BP372	BP793	BP795	BP796	BP805	BP830
BP881	BP931	BP955	BP961	BP971	BP1008
BP1014	BP1024	BP1025	BP1027	BP1028	BP1029
BP1030	BP1031	BP1032	BP1033	BP1034	. . .

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

	COMMENTS	`Left examples have the keyword "leftright" on the OEBP.`
	CROSSREFS	`See updown.` `All "leftright" Bongard Problems are handed.` `Adjacent-numbered pages: BP530 BP531 BP532 BP533 BP534 * BP536 BP537 BP538 BP539 BP540`
	KEYWORD	`meta (see left/right), links, keyword, sideless, invariance`
	WORLD	`handed_visualbp [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`

BP537

Meta Bongard Problems vs. other Bongard Problems.

BP200	BP501	BP503	BP504	BP506	BP507
BP508	BP509	BP510	BP511	BP512	BP513
BP514	BP515	BP516	BP517	BP518	BP519
BP520	BP521	BP522	BP526	BP534	BP535
BP537	BP539	BP541	BP542	BP544	BP546
BP547	BP549	BP550	BP552	BP553	. . .

	BP1	BP2	BP3	BP4	BP5	BP6
	BP7	BP8	BP9	BP10

?
BP1080

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

	COMMENTS	`Bongard Problems sorted left have the keyword "meta" on the OEBP.` `Meta Bongard Problems are Bongard Problems that sort Bongard Problems. Sometimes abbreviated MBPs.` `The first meta Bongard Problem was BP200.` `Some meta BP pages sort images of Bongard Problems (keyword miniproblems), while other meta BP pages sort other BP pages (keyword links).`
	CROSSREFS	`BPs that sort meta-BPs are labelled metameta.` `Adjacent-numbered pages: BP532 BP533 BP534 BP535 BP536 * BP538 BP539 BP540 BP541 BP542`
	KEYWORD	`meta (see left/right), links, keyword, world, left-self, sideless, metameta, left-full, feedback`
	CONCEPT	`recursion (info \| search)`
	WORLD	`bp [smaller \| same \| bigger] zoom in left (linksbp)`
	AUTHOR	`Aaron David Fairbanks`

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