The On-Line Encyclopedia of Bongard Problems

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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`

Closed shape outline vs. non-closed curve.

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	COMMENTS	`All examples in this Bongard Problem are non-self-intersecting curves.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`Adjacent-numbered pages: BP10 BP11 BP12 BP13 BP14 * BP16 BP17 BP18 BP19 BP20`
	KEYWORD	`nice, unstable, world, finished, traditional, bongard`
	CONCEPT	`closed_open (info \| search),` `hole (info \| search),` `loop (info \| search)`
	WORLD	`curve_or_outline [smaller \| same \| bigger] zoom in left (shape_outline) \| zoom in right (curve)`
	AUTHOR	`Mikhail M. Bongard`

Clockwise spiraling curve vs. counter-clockwise spiraling curve.

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	COMMENTS	`All examples in this Bongard Problem are non-self-intersecting spiraling curves, perhaps wiggly, perhaps with corners.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.`
	CROSSREFS	`Adjacent-numbered pages: BP11 BP12 BP13 BP14 BP15 * BP17 BP18 BP19 BP20 BP21`
	KEYWORD	`nice, handed, gap, finished, traditional, bongard`
	CONCEPT	`turn_orientation (info \| search),` `tracing_line_or_curve (info \| search),` `rotational_direction (info \| search),` `direction (info \| search)`
	WORLD	`spiral [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

A curve with one self-crossing vs. a curve without a self-crossing.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.`
	CROSSREFS	`BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.` `Adjacent-numbered pages: BP25 BP26 BP27 BP28 BP29 * BP31 BP32 BP33 BP34 BP35`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`x-crossing (info \| search),` `existence (info \| search)`
	WORLD	`crosscurve [smaller \| same \| bigger] zoom in right (curve_or_outline)`
	AUTHOR	`Mikhail M. Bongard`

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`

Ends of the curve are far apart vs. ends of the curve are close together.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.`
	CROSSREFS	`Adjacent-numbered pages: BP57 BP58 BP59 BP60 BP61 * BP63 BP64 BP65 BP66 BP67`
	KEYWORD	`nice, fuzzy, spectrum, stretch, stable, finished, traditional, continuous, bongard`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `near_far (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Ends of the curve are parallel vs. ends of the curve are perpendicular.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.`
	CROSSREFS	`Adjacent-numbered pages: BP67 BP68 BP69 BP70 BP71 * BP73 BP74 BP75 BP76 BP77`
	KEYWORD	`nice, precise, unstable, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`slope_at_endpoint (info \| search),` `tracing_line_or_curve (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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`

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`

Same curvature close to the middle vs. change of curvature close to the middle.

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	CROSSREFS	`Adjacent-numbered pages: BP178 BP179 BP180 BP181 BP182 * BP184 BP185 BP186 BP187 BP188`
	KEYWORD	`noisy, traditional`
	CONCEPT	`sides_of_line (info \| search),` `tangent (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

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