The On-Line Encyclopedia of Bongard Problems

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BP50

Vertical axis of symmetry vs. no axis of symmetry.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`BP152 is the same solution (with the sides switched), using connected shapes and without black filling.` `BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)` `Adjacent-numbered pages: BP45 BP46 BP47 BP48 BP49 * BP51 BP52 BP53 BP54 BP55`
	KEYWORD	`nice, stretch, left-narrow, finished, traditional, bongard`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`curves_and_fill_shapes_separate_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP152

No axis of symmetry vs. vertical axis of symmetry.

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	CROSSREFS	`BP50 is the same solution (with the sides switched), using multiple shapes and with some shapes filled in black.` `BP1206 is like BP50 but instead of "no axis of symmetry at all" it uses "no vertical axis of symmetry".` `Adjacent-numbered pages: BP147 BP148 BP149 BP150 BP151 * BP153 BP154 BP155 BP156 BP157`
	KEYWORD	`rotate, stretch, traditional`
	CONCEPT	`existence (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP172

Rotationally symmetric vs. not.

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	COMMENTS	`The rotational symmetry axis is about the center of the object, not the bounding box. Positioning within the bounding box is noise.`
	CROSSREFS	`Adjacent-numbered pages: BP167 BP168 BP169 BP170 BP171 * BP173 BP174 BP175 BP176 BP177`
	KEYWORD	`traditional`
	CONCEPT	`rotational_symmetry (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP265

Axis of symmetry vs. no axis of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP260 BP261 BP262 BP263 BP264 * BP266 BP267 BP268 BP269 BP270`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP269

Center of symmetry vs. no center of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP264 BP265 BP266 BP267 BP268 * BP270 BP271 BP272 BP273 BP274`
	CONCEPT	`symmetry (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP342

Exactly one axis of symmetry vs. either zero or more than one axis of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP337 BP338 BP339 BP340 BP341 * BP343 BP344 BP345 BP346 BP347`
	KEYWORD	`traditional, finishedexamples`
	CONCEPT	`exists_one (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP811

Archimedean tiling (regular polygons, all vertices look the same) versus two-uniform tiling (regular polygons, two different kinds of vertex).

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	CROSSREFS	`Adjacent-numbered pages: BP806 BP807 BP808 BP809 BP810 * BP812 BP813 BP814 BP815 BP816`
	KEYWORD	`nice, math`
	CONCEPT	`infinite_plane (info \| search),` `tiling (info \| search),` `symmetry (info \| search)`
	WORLD	`wallpaper_tiling [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP847

Evokes the idea of symmetry vs. not so.

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	COMMENTS	`Or, perhaps more concretely, "Depiction of object with some symmetry (invariance under transformation) vs. depiction of object with no simple symmetries."`
	CROSSREFS	`Adjacent-numbered pages: BP842 BP843 BP844 BP845 BP846 * BP848 BP849 BP850 BP851 BP852`
	KEYWORD	`nice, fuzzy, abstract, math, concept, collective, dithering`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

BP869

Approximately symmetric vs. asymmetric.

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	COMMENTS	`Or, "evokes idea of symmetry (see BP760) vs. not so," which is also a solution for BP847. - Aaron David Fairbanks, Jul 29 2020`
	CROSSREFS	`Adjacent-numbered pages: BP864 BP865 BP866 BP867 BP868 * BP870 BP871 BP872 BP873 BP874`
	KEYWORD	`abstract, spectrum, anticomputer, subjective, concept, perfect`
	CONCEPT	`imperfection_small (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

BP986

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)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

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