The On-Line Encyclopedia of Bongard Problems

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BP14

All big individual figures vs. all small individual figures.

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	COMMENTS	`All examples in this Problem show one or more connected figures made up of lines.` `Some big shapes and some small shapes would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`See BP2 for the same idea using one shape.` `Adjacent-numbered pages: BP9 BP10 BP11 BP12 BP13 * BP15 BP16 BP17 BP18 BP19`
	KEYWORD	`fuzzy, size, stable, finished, traditional, bongard`
	CONCEPT	`all (info \| search),` `length_line_or_curve (info \| search),` `size (info \| search)`
	WORLD	`curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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`

BP91

Three identical elements vs. four identical elements.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`BP1226 is "three identical elements vs. other number of identical elements".` `Adjacent-numbered pages: BP86 BP87 BP88 BP89 BP90 * BP92 BP93 BP94 BP95 BP96`
	KEYWORD	`number, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`indentation (info \| search),` `on_line_or_curve (info \| search),` `number (info \| search),` `protrusion (info \| search),` `separation_of_joined_objects (info \| search),` `same (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`curves_and_fill_shapes_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP119

A small correction will result in a single circle vs. no small correction will result in a single circle.

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	CROSSREFS	`Adjacent-numbered pages: BP114 BP115 BP116 BP117 BP118 * BP120 BP121 BP122 BP123 BP124`
	KEYWORD	`fuzzy, traditional`
	CONCEPT	`existence (info \| search),` `imperfection_small (info \| search)`
	WORLD	`curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

BP541

Bongard Problems vs. anything else.

BP1

BP2

BP3

BP4

BP541

BP1073

blllmam

cat

nongard

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	COMMENTS	`This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.`
	CROSSREFS	`Adjacent-numbered pages: BP536 BP537 BP538 BP539 BP540 * BP542 BP543 BP544 BP545 BP546`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bp)`
	AUTHOR	`Aaron David Fairbanks`

BP542

BP Pages on the OEBP vs. anything else.

BP1

BP2

BP3

BP542

BP1073

BP0

nolab

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	CROSSREFS	`Adjacent-numbered pages: BP537 BP538 BP539 BP540 BP541 * BP543 BP544 BP545 BP546 BP547`
	KEYWORD	`notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bppage)`
	AUTHOR	`Aaron David Fairbanks`

BP544

Everything vs. nothing.

	&(%	0	BP1	BP544	BP1073
		dog	nothing

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	COMMENTS	`All ideas and things, with no limits.`
	CROSSREFS	`Adjacent-numbered pages: BP539 BP540 BP541 BP542 BP543 * BP545 BP546 BP547 BP548 BP549`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny`
	CONCEPT	`existence (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (everything) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

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	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

BP810

Figures can be transformed into one another by smooth stretching (intersection points stay constant; paths connecting those points remain), while remaining within the 2d box vs. movement out of the plane required.

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	CROSSREFS	`All examples here fit left in BP809, a version where the figures are allowed to pass through themselves while being deformed.` `Adjacent-numbered pages: BP805 BP806 BP807 BP808 BP809 * BP811 BP812 BP813 BP814 BP815`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_homeomorphic_figures_made_of_curves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP851

Figure with points (small white circles) can be smoothly deformed within the 2D plane without passing through itself so that all points touch to make the other figure vs. not so (movement out of the plane required).

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	CROSSREFS	`All examples here fit left in BP369, a version where the figure is allowed to pass through itself while being deformed.` `Adjacent-numbered pages: BP846 BP847 BP848 BP849 BP850 * BP852 BP853 BP854 BP855 BP856`
	KEYWORD	`math, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`figure_made_of_curves_and_quotient_by_hollow_dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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