The On-Line Encyclopedia of Bongard Problems

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BP355

Fractal iteration based on 2-D (shapes) vs. fractal iteration based on 1-D (line segments).

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	CROSSREFS	`Adjacent-numbered pages: BP350 BP351 BP352 BP353 BP354 * BP356 BP357 BP358 BP359 BP360`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`fractal (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_fractal_iterate_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP356

Object at lower-right fits as n-th item in the top row of objects, where n is the number of dots at lower-left vs. not so.

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	COMMENTS	`All examples have a number of dots in the bottom left corner, an object in the bottom right corner, and a sequence of object at the top.`
	CROSSREFS	`Adjacent-numbered pages: BP351 BP352 BP353 BP354 BP355 * BP357 BP358 BP359 BP360 BP361`
	KEYWORD	`nice, creativeexamples, left-narrow, structure, traditional, rules, miniworlds`
	CONCEPT	`fractal (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search),` `feature_cluster (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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`

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`

BP1002

Vaguely self-similar (looks like self-similar fractal after one iteration) vs. not so.

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	CROSSREFS	`See BP1004 for a Problem about conceptual self-similarity instead of visual self-similarity.` `See BP188 for a similar Problem restricted to shape outlines made of shape outlines.` `Adjacent-numbered pages: BP997 BP998 BP999 BP1000 BP1001 * BP1003 BP1004 BP1005 BP1006 BP1007`
	KEYWORD	`easy, nice, fuzzy, abstract, anticomputer, concept, traditional`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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