The On-Line Encyclopedia of Bongard Problems

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The chain does not branch vs. the chain branches.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`Adjacent-numbered pages: BP87 BP88 BP89 BP90 BP91 * BP93 BP94 BP95 BP96 BP97`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`all (info \| search),` `branch_point (info \| search),` `collinear (info \| search),` `existence (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Triangle inside of the circle vs. circle inside of the triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.`
	CROSSREFS	`Adjacent-numbered pages: BP42 BP43 BP44 BP45 BP46 * BP48 BP49 BP50 BP51 BP52`
	KEYWORD	`finished, traditional, viceversa, bongard`
	CONCEPT	`inside (info \| search),` `triangle (info \| search)`
	WORLD	`circle_triangle_outlines_nest [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

If you place the image on top of itself so that it lines up with itself exactly within a small region, it also lines up everywhere else vs. not so.

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	COMMENTS	`Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.` `Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.`
	CROSSREFS	`See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.` `Adjacent-numbered pages: BP960 BP961 BP962 BP963 BP964 * BP966 BP967 BP968 BP969 BP970`
	KEYWORD	`hard, precise, distractingworld, perfect`
	CONCEPT	`local_global (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

All points (small white circles) on one figure can be glued together to make the other figure vs. not so.

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	CROSSREFS	`See BP851 for a version where the figure must stay within the 2D plane and cannot pass through itself while being deformed.` `Adjacent-numbered pages: BP364 BP365 BP366 BP367 BP368 * BP370 BP371 BP372 BP373 BP374`
	KEYWORD	`math`
	CONCEPT	`topological_transformation (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`zoom in left (figure_made_of_curves_and_quotient_by_hollow_dots)`
	AUTHOR	`Aaron David Fairbanks`

Square bounding box vs. oblong rectangular bounding box.

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	CROSSREFS	`Adjacent-numbered pages: BP937 BP938 BP939 BP940 BP941 * BP943 BP944 BP945 BP946 BP947`
	KEYWORD	`precise, stretch, boundingbox, invalid, experimental, preciseworld`
	CONCEPT	`bounding_box (info \| search),` `square (info \| search)`
	WORLD	`rectangular_arrangement_of_white_pixels [smaller \| same \| bigger] zoom in left (square_arrangement_of_white_pixels) \| zoom in right (oblong_rectangular_arrangement_of_white_pixels)`
	AUTHOR	`Leo Crabbe`

The two points are reachable through a path vs. the two points are unreachable by any path.

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	CROSSREFS	`Adjacent-numbered pages: BP289 BP290 BP291 BP292 BP293 * BP295 BP296 BP297 BP298 BP299`
	KEYWORD	`traditional`
	CONCEPT	`maze (info \| search),` `path (info \| search),` `reachable (info \| search)`
	AUTHOR	`"Lewis"`

There is an infinite one-one-one-one-... chain present vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1062 BP1063 BP1064 BP1065 BP1066 * BP1068 BP1069 BP1070 BP1071 BP1072`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Three or more small clusters of dots vs. not so.

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	CROSSREFS	`BP307 is similar.` `Adjacent-numbered pages: BP303 BP304 BP305 BP306 BP307 * BP309 BP310 BP311 BP312 BP313`
	KEYWORD	`traditional`
	CONCEPT	`feature_cluster (info \| search),` `cluster (info \| search),` `three (info \| search)`
	AUTHOR	`"Lewis"`

Unconnected circles on a horizontal line vs. unconnected circles on a vertical line.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.`
	CROSSREFS	`Adjacent-numbered pages: BP61 BP62 BP63 BP64 BP65 * BP67 BP68 BP69 BP70 BP71`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `horizontal (info \| search),` `on_line_or_curve (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `vertical (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Three parts vs. five parts.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.`
	CROSSREFS	`Adjacent-numbered pages: BP84 BP85 BP86 BP87 BP88 * BP90 BP91 BP92 BP93 BP94`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `three (info \| search),` `five (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

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