The On-Line Encyclopedia of Bongard Problems

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BP1065

All boxes on each particular nesting depth have the same number of boxes in them vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1060 BP1061 BP1062 BP1063 BP1064 * BP1066 BP1067 BP1068 BP1069 BP1070`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1066

Some region has one box in it vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1061 BP1062 BP1063 BP1064 BP1065 * BP1067 BP1068 BP1069 BP1070 BP1071`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `one (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1067

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

(edit; present; nest [left/right]; search; history)

	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`

BP1068

Every nonempty region has two boxes vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1063 BP1064 BP1065 BP1066 BP1067 * BP1069 BP1070 BP1071 BP1072 BP1073`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1069

Infinitely many branches vs. finitely many branches.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1064 BP1065 BP1066 BP1067 BP1068 * BP1070 BP1071 BP1072 BP1073 BP1074`
	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`

BP1070

Dead end vs. no dead ends.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1065 BP1066 BP1067 BP1068 BP1069 * BP1071 BP1072 BP1073 BP1074 BP1075`
	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`

BP1071

Two of the same kind within in one region vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`See BP977 for a version without infinite nesting and other drawings than boxes.` `Adjacent-numbered pages: BP1066 BP1067 BP1068 BP1069 BP1070 * BP1072 BP1073 BP1074 BP1075 BP1076`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1077

All regions have the same number of boxes vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1072 BP1073 BP1074 BP1075 BP1076 * BP1078 BP1079 BP1080 BP1081 BP1082`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1107

Contains smaller copy of self with black and white inverted vs. not so.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`There are various problematic cases left out. Are black and white to be inverted within a fractal's convex hull or its outermost outline?` `Must this outline be preserved around the smaller inverted version of the fractal, or is it allowed to bleed into other white areas?` `No examples have been included in this Bongard Problem whose placement depends on these questions.`
	CROSSREFS	`Adjacent-numbered pages: BP1102 BP1103 BP1104 BP1105 BP1106 * BP1108 BP1109 BP1110 BP1111 BP1112`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`black_white_inversion (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1108

Solid chunk of black space in neighborhood of any point of the fractal vs. solid chunk of white space in any neighborhood.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP1103 BP1104 BP1105 BP1106 BP1107 * BP1109 BP1110 BP1111 BP1112 BP1113`
	KEYWORD	`right-null, perfect, infinitedetail, assumesfamiliarity, neither`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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