The On-Line Encyclopedia of Bongard Problems

Search: ex:EX8974

Displaying 1-4 of 4 results found.

page 1

Sort: id Format: long Filter: (all | no meta | meta) Mode: (words | no words)

Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself.

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

	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`

Contains smaller copy of self with black and white inverted vs. not so.

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

	COMMENTS	`There are various problematic cases left out. Are black and white to be inverted within a fractal's convex hull or its outermost outline?` `Must this outline be preserved around the smaller inverted version of the fractal, or is it allowed to bleed into other white areas?` `No examples have been included in this Bongard Problem whose placement depends on these questions.`
	CROSSREFS	`Adjacent-numbered pages: BP1102 BP1103 BP1104 BP1105 BP1106 * BP1108 BP1109 BP1110 BP1111 BP1112`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`black_white_inversion (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Solid chunk of black space in neighborhood of any point of the fractal vs. solid chunk of white space in any neighborhood.

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

	CROSSREFS	`Adjacent-numbered pages: BP1103 BP1104 BP1105 BP1106 BP1107 * BP1109 BP1110 BP1111 BP1112 BP1113`
	KEYWORD	`right-null, perfect, infinitedetail, assumesfamiliarity, neither`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Tiled by finitely many smaller copies of itself (different sizes allowed) vs. not so.

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

	COMMENTS	`These are sometimes called "irreptiles".`
	CROSSREFS	`See BP532 for the version with only one size of tile allowed.` `Adjacent-numbered pages: BP1114 BP1115 BP1116 BP1117 BP1118 * BP1120 BP1121 BP1122 BP1123 BP1124`
	KEYWORD	`hardsort, proofsrequired, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

page 1

		Hints
(Greetings from The On-Line Encyclopedia of Bongard Problems!)