The On-Line Encyclopedia of Bongard Problems

Search: concept:self-reference

Displaying 41-50 of 55 results found.

( prev | next ) page 1 2 3 4 5 6

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

BP1098

Concave shapes whose cavities are similar to the shape vs. concave shape whose cavities are not similar to the shape.

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

	COMMENTS	`"I am agnostic on whether to let this world include examples such as EX8932, where pixelation is used, or examples such as suggested by EX8928 similar to the "Topologist's Comb" (link in references) which are not locally path-connected. These two examples were provided by Aaron David Fairbanks." - Jago Collins 28th January 2021`
	REFERENCE	`https://en.wikipedia.org/wiki/Similarity_(geometry)` `https://en.wikipedia.org/wiki/Self-similarity` `https://en.wikipedia.org/wiki/Comb_space`
	CROSSREFS	`Adjacent-numbered pages: BP1093 BP1094 BP1095 BP1096 BP1097 * BP1099 BP1100 BP1101 BP1102 BP1103`
	EXAMPLE	`A circle with a circle cut out of it does not fit left, because with the circle cut out of it, our shape is no longer a circle.`
	KEYWORD	`stub, precise, allsorted, left-narrow, perfect, infinitedetail`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Jago Collins`

BP1107

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`

BP1108

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`

BP1114

Fractals contain one another vs. only one contains the other.

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

	CROSSREFS	`Adjacent-numbered pages: BP1109 BP1110 BP1111 BP1112 BP1113 * BP1115 BP1116 BP1117 BP1118 BP1119`
	KEYWORD	`perfect, infinitedetail, unorderedpair`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1115

Fractals tile one another vs. not so (fractals are rather tiled by some combination of one another and themselves).

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

	COMMENTS	`Rotations and reflections avoided in all examples for simplicity.`
	CROSSREFS	`Adjacent-numbered pages: BP1110 BP1111 BP1112 BP1113 BP1114 * BP1116 BP1117 BP1118 BP1119 BP1120`
	KEYWORD	`perfect, infinitedetail, unorderedpair`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1116

Contains self somewhere within any area around any point within self vs. not so.

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

	COMMENTS	`Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".` `The left hand side of this is a weaker condition than the left hand side of BP1241.`
	CROSSREFS	`Adjacent-numbered pages: BP1111 BP1112 BP1113 BP1114 BP1115 * BP1117 BP1118 BP1119 BP1120 BP1121`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1118

Self-similar only scaled about one point vs. multiple centers of self-similarity.

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

	COMMENTS	`There is only ever one such center of self-similarity or infinitely many.`
	CROSSREFS	`Adjacent-numbered pages: BP1113 BP1114 BP1115 BP1116 BP1117 * BP1119 BP1120 BP1121 BP1122 BP1123`
	KEYWORD	`nice, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1119

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`

BP1120

No same-sized copies of self overlap vs. distinct same-sized copies overlap.

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

	COMMENTS	`With mathematical jargon:` `No distinct same-sized copies of self overlap on a subset with positive measure in the Hausdorff measure using the Hausdorff dimension.` `For a covering of a fractal by finitely many scaled down copies of itself, the condition of that no two have an intersection with positive measure is equivalent to the condition that the Hausdorff dimension coincides with the similarity dimension.` `(There is another similar condition in this context called the "open set condition" which implies this but is not equivalent. The open set condition is equivalent to the condition that the Hausdorff measure using the similarity dimension is nonzero.)`
	REFERENCE	`https://en.wikipedia.org/wiki/Hausdorff_dimension` `https://en.wikipedia.org/wiki/Open_set_condition`
	CROSSREFS	`Adjacent-numbered pages: BP1115 BP1116 BP1117 BP1118 BP1119 * BP1121 BP1122 BP1123 BP1124 BP1125`
	KEYWORD	`challenge, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1122

Content of any square is an image of the whole panel vs. not so.

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

	CROSSREFS	`Similar to BP818.` `Adjacent-numbered pages: BP1117 BP1118 BP1119 BP1120 BP1121 * BP1123 BP1124 BP1125 BP1126 BP1127`
	KEYWORD	`nice, minimal, size, boundingbox, infinitedetail, preciseworld, absoluteposition`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

( prev | next ) page 1 2 3 4 5 6

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