The On-Line Encyclopedia of Bongard Problems

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BP1118

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

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	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.

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	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.

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	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.

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	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`

BP1147

Columns of the table could be respectively labeled "Number" and "Number of times number appears in this table" vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1142 BP1143 BP1144 BP1145 BP1146 * BP1148 BP1149 BP1150 BP1151 BP1152`
	KEYWORD	`nice, precise, notso, handed, leftright, left-narrow, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1148

Number of dots in the Nth box (from the left) is how many times the number (N - 1) appears in the whole diagram vs. not so.

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	COMMENTS	`Left-sorted examples are sometimes called autobiographical or self-descriptive numbers.`
	REFERENCE	`https://oeis.org/A349595` `https://en.wikipedia.org/wiki/Self-descriptive_number`
	CROSSREFS	`See BP1147 for a similar idea.` `BP1149 was inspired by this.` `Adjacent-numbered pages: BP1143 BP1144 BP1145 BP1146 BP1147 * BP1149 BP1150 BP1151 BP1152 BP1153`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1149

Number in the Nth box (from the left) is how many numbers appear N times vs. not so.

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	CROSSREFS	`Inspired by BP1148.` `Adjacent-numbered pages: BP1144 BP1145 BP1146 BP1147 BP1148 * BP1150 BP1151 BP1152 BP1153 BP1154`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1241

Any point contained in (arbitrarily) smaller version of self vs. not so.

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	COMMENTS	`Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.` `It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)` `The left hand side of this is a stronger condition than the left hand side of BP1116.`
	CROSSREFS	`Adjacent-numbered pages: BP1236 BP1237 BP1238 BP1239 BP1240 * BP1242 BP1243 BP1244 BP1245 BP1246`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1246

Any symmetry exhibited by some non-empty subset of the objects is also a symmetry of the whole thing vs. not so.

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	COMMENTS	`In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.`
	CROSSREFS	`See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.` `Adjacent-numbered pages: BP1241 BP1242 BP1243 BP1244 BP1245 * BP1247 BP1248 BP1249 BP1250 BP1251`
	KEYWORD	`precise, allsorted, unwordable, notso, traditional`
	CONCEPT	`local_global (info \| search),` `self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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