The On-Line Encyclopedia of Bongard Problems

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Image contains the exact arrangement of pixels that form the "S" creature depicted in EX9532 vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1156 BP1157 BP1158 BP1159 BP1160 * BP1162 BP1163 BP1164 BP1165 BP1166`
	KEYWORD	`unwordable, notso, arbitrary, handed, leftright, updown, stretch, blackwhite, creativeexamples, right-null, perfect, pixelperfect, help`
	AUTHOR	`Leo Crabbe`

BP1227

Appears on its own right side vs. does not.

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	COMMENTS	`This was created as an example of a Bongard Problem that could include an image of a Bongard Problem with the same solution as itself but could not include the very image of itself (appearing within itself fractally).`
	CROSSREFS	`See also BP961, "appears on its own left side vs. appears on its own right side".` `Adjacent-numbered pages: BP1222 BP1223 BP1224 BP1225 BP1226 * BP1228 BP1229 BP1230 BP1231 BP1232`
	KEYWORD	`stub, precise, allsorted, notso, handed, leftright, example, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1230

Invariant under scaling by a certain amount vs. not.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1225 BP1226 BP1227 BP1228 BP1229 * BP1231 BP1232 BP1233 BP1234 BP1235`
	KEYWORD	`stub, notso, perfect, infinitedetail, left-couldbe, bordercontent`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1237

Connected fractal vs. disconnected fractal.

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	CROSSREFS	`Adjacent-numbered pages: BP1232 BP1233 BP1234 BP1235 BP1236 * BP1238 BP1239 BP1240 BP1241 BP1242`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`connected_component (info \| search),` `fractal (info \| search)`
	WORLD	`fractal_self_tile [smaller \| same \| bigger] zoom in left (connected_fractal_self_tile)`
	AUTHOR	`Jago Collins`

BP1238

Fractal with hole vs. fractal with no hole (simply connected).

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	CROSSREFS	`Adjacent-numbered pages: BP1233 BP1234 BP1235 BP1236 BP1237 * BP1239 BP1240 BP1241 BP1242 BP1243`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`existence (info \| search),` `fractal (info \| search),` `hole (info \| search),` `loop (info \| search)`
	WORLD	`connected_fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1239

Fractal topologically closed (each white point has a neighborhood of pure white surrounding it) vs. not

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	COMMENTS	`It isn't possible to unambiguously communicate whether or not a few specific points are missing.`
	CROSSREFS	`Adjacent-numbered pages: BP1234 BP1235 BP1236 BP1237 BP1238 * BP1240 BP1241 BP1242 BP1243 BP1244`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`fractal (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`

BP1242

Tiled by pair of fractals including itself such that both tile the other vs. tiled by pair of fractals including itself such that the other tiles itself.

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	COMMENTS	`Proofs still needed that all the examples on the left hand side cannot fit on the right hand side as well, and that EX9881 cannot fit on the left hand side as well.`
	CROSSREFS	`The left hand side implies the left hand side of BP1116.` `The right hand side does not imply the right hand side of BP1116. (EX9881 is meant to be a counterexample.)` `Adjacent-numbered pages: BP1237 BP1238 BP1239 BP1240 BP1241 * BP1243 BP1244 BP1245 BP1246 BP1247`
	KEYWORD	`unwordable, overriddensolution, perfect, infinitedetail, both, missingproofs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1244

Tiled by self-tiling fractal vs. not

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	COMMENTS	`Proofs are still needed for examples fitting right.` `EX9875 is tiled by Sierpinski triangles, but this requires the Sierpinski triangle tiles' bounding triangles to overlap.`
	CROSSREFS	`Self-tiling fractals (BP532^left) are all sorted left.` `Adjacent-numbered pages: BP1239 BP1240 BP1241 BP1242 BP1243 * BP1245 BP1246 BP1247 BP1248 BP1249`
	KEYWORD	`notso, perfect, infinitedetail, missingproofs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1248

No straight path passes from a white region to a grey one, then to white again (without hitting black) vs. such a path exists.

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	CROSSREFS	`Adjacent-numbered pages: BP1243 BP1244 BP1245 BP1246 BP1247 * BP1249 BP1250 BP1251 BP1252 BP1253`
	KEYWORD	`precise, allsorted, unwordable, notso, perfect`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

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