The On-Line Encyclopedia of Bongard Problems

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Solid dark circle not at end vs. solid dark circle at end.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.`
	CROSSREFS	`Adjacent-numbered pages: BP89 BP90 BP91 BP92 BP93 * BP95 BP96 BP97 BP98 BP99`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`between (info \| search),` `collinear (info \| search),` `line_or_curve_endpoint (info \| search),` `outlined_filled (info \| search),` `separation_of_joined_objects (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Points located at the same distances from a cross vs. points located at different distances from a cross.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 240.`
	CROSSREFS	`Adjacent-numbered pages: BP75 BP76 BP77 BP78 BP79 * BP81 BP82 BP83 BP84 BP85`
	KEYWORD	`stretch, finished, traditional, bongard`
	CONCEPT	`length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Image of a Bongard Problem with (left) solution property that can have multiplicity vs. not so.

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	COMMENTS	`All examples are "object present vs. object absent" Problems.`
	CROSSREFS	`Adjacent-numbered pages: BP828 BP829 BP830 BP831 BP832 * BP834 BP835 BP836 BP837 BP838`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`existence (info \| search),` `number (info \| search),` `one (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Black shape is a valid shadow (2D projection) of 3D shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP895 BP896 BP897 BP898 BP899 * BP901 BP902 BP903 BP904 BP905`
	KEYWORD	`3d, orderedpair`
	CONCEPT	`3d_solid (info \| search),` `projection (info \| search)`
	AUTHOR	`Leo Crabbe`

Circle and two vertices are collinear vs. no two vertices and the circle are collinear.

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	CROSSREFS	`Adjacent-numbered pages: BP249 BP250 BP251 BP252 BP253 * BP255 BP256 BP257 BP258 BP259`
	KEYWORD	`traditional`
	CONCEPT	`collinear (info \| search),` `vertex_of_meeting_lines (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

More solid black figures vs. more outline figures.

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	COMMENTS	`All small squares appearing in this problem are axis-aligned.` `All examples have at least one filled shape and one outline.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.`
	CROSSREFS	`Adjacent-numbered pages: BP22 BP23 BP24 BP25 BP26 * BP28 BP29 BP30 BP31 BP32`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `texture (info \| search),` `quantity_comparison (info \| search)`
	WORLD	`circle_square_eq-tri_small_some_outline_some_fill [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Some zoomed-in (cropped) version of an image of a hollow circle vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP520 BP521 BP522 BP523 BP524 * BP526 BP527 BP528 BP529 BP530`
	KEYWORD	`stretch, boundingbox, left-null, traditional, left-couldbe`
	CONCEPT	`circle (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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`

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, both`
	CONCEPT	`diagonal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Convex hull is a square vs. convex hull is not a square.

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	COMMENTS	`Additionally, the points in the examples on the left lie on the boundary of the square.` `EX2897 was originally on the right hand side, but it was removed because it seems to be an error.`
	CROSSREFS	`Adjacent-numbered pages: BP237 BP238 BP239 BP240 BP241 * BP243 BP244 BP245 BP246 BP247`
	KEYWORD	`noisy, traditional`
	CONCEPT	`convex_hull (info \| search),` `square (info \| search)`
	AUTHOR	`Matthew J. Howells`

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