The On-Line Encyclopedia of Bongard Problems

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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`

Increasing quantity loops back to starting value vs. increasing quantity cannot loop back to starting value.

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	CROSSREFS	`Adjacent-numbered pages: BP348 BP349 BP350 BP351 BP352 * BP354 BP355 BP356 BP357 BP358`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules, miniworlds`
	CONCEPT	`iteration (info \| search),` `loop (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in left (constant_change_seq_loop_right)`
	AUTHOR	`Aaron David Fairbanks`

Increasing quantity is angular vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP349 BP350 BP351 BP352 BP353 * BP355 BP356 BP357 BP358 BP359`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules, miniworlds`
	CONCEPT	`angle (info \| search),` `loop (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Graph contains a "loop" a.k.a. cycle (cyclic) versus graph is acyclic.

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	CROSSREFS	`Adjacent-numbered pages: BP783 BP784 BP785 BP786 BP787 * BP789 BP790 BP791 BP792 BP793`
	KEYWORD	`nice, precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Every vertex is connected to every other vs. vertices are connected in a cycle (no other connections).

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	COMMENTS	`Complete graphs with zero, one, two, or three vertices would be ambiguously categorized (fit in overlap of both sides).` `Left examples are called "fully connected graphs." Right examples are called "cycle graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP927 BP928 BP929 BP930 BP931 * BP933 BP934 BP935 BP936 BP937`
	KEYWORD	`precise, left-narrow, right-narrow, both, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Fractal with hole vs. fractal with no hole (simply connected).

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	CROSSREFS	`Adjacent-numbered pages: BP1233 BP1234 BP1235 BP1236 BP1237 * BP1239 BP1240 BP1241 BP1242 BP1243`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`closed_open (info \| search),` `existence (info \| search),` `fractal (info \| search),` `hole (info \| search),` `loop (info \| search)`
	WORLD	`connected_fractal_self_tile [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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