The On-Line Encyclopedia of Bongard Problems

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Palindromes vs. not palindromes.

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	COMMENTS	`All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."`
	CROSSREFS	`Adjacent-numbered pages: BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991`
	KEYWORD	`nice, precise, allsorted, notso, sequence, traditional`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Jago Collins`

Vertical axis of symmetry vs. no vertical axis of symmetry.

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	COMMENTS	`This was created to be a slightly different version of BP50, "vertical axis of symmetry vs. no axis of symmetry". The solution for this Bongard Problem is also a (less specific) solution for BP50.`
	CROSSREFS	`BP1207 is the same solution but using the horizontal axis instead of the vertical axis.` `BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.` `Adjacent-numbered pages: BP1201 BP1202 BP1203 BP1204 BP1205 * BP1207 BP1208 BP1209 BP1210 BP1211`
	KEYWORD	`stub, notso, stretch, left-narrow, traditional`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `vertical (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Horizontal axis of symmetry vs. no horizontal axis of symmetry.

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	CROSSREFS	`BP1206 is the same solution but using the vertical axis instead of the horizontal axis.` `BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.` `Adjacent-numbered pages: BP1202 BP1203 BP1204 BP1205 BP1206 * BP1208 BP1209 BP1210 BP1211 BP1212`
	KEYWORD	`stub, notso, stretch, left-narrow, traditional`
	CONCEPT	`horizontal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Vertical, horizontal, and both diagonal axes of symmetry vs. not (more specifically, one or fewer axes of symmetry).

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	CROSSREFS	`Adjacent-numbered pages: BP1205 BP1206 BP1207 BP1208 BP1209 * BP1211 BP1212 BP1213 BP1214 BP1215`
	KEYWORD	`stub, left-narrow, traditional`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `four (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Axis of symmetry along the NW/SE diagonal vs. axis of symmetry along the NE/SW diagonal

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	CROSSREFS	`Adjacent-numbered pages: BP1208 BP1209 BP1210 BP1211 BP1212 * BP1214 BP1215 BP1216 BP1217 BP1218`
	KEYWORD	`stub, dual, handed, leftright, updown, rotate, stretch, left-narrow, right-narrow, traditional`
	CONCEPT	`diagonal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Axis of symmetry along the NW/SE diagonal vs. not.

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	CROSSREFS	`BP1206 is the same solution but with the vertical axis instead of the NW/SE diagonal.` `BP1207 is the same solution but with the horizontal axis instead of the NW/SE diagonal.` `Adjacent-numbered pages: BP1210 BP1211 BP1212 BP1213 BP1214 * BP1216 BP1217 BP1218 BP1219 BP1220`
	KEYWORD	`stub, notso, handed, leftright, updown, rotate, left-narrow, traditional`
	CONCEPT	`diagonal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Frieze pattern with glide reflection symmetry vs. not.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1223 BP1224 BP1225 BP1226 BP1227 * BP1229 BP1230 BP1231 BP1232 BP1233`
	KEYWORD	`stub, notso, traditional, bordercontent, seemslike`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Translational symmetry vs. no translational symmetry.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1224 BP1225 BP1226 BP1227 BP1228 * BP1230 BP1231 BP1232 BP1233 BP1234`
	KEYWORD	`stub, notso, seemslike`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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`

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	`self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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