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BP953 Image of this Bongard Problem vs. empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes.

CROSSREFS

See BP959, BP902.

Adjacent-numbered pages:
BP948 BP949 BP950 BP951 BP952  *  BP954 BP955 BP956 BP957 BP958

KEYWORD

nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

zoom in left (bp953_image) | zoom in right (blank_image)

AUTHOR

Leo Crabbe

BP956 Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).
(edit; present; nest [left/right]; search; history)
COMMENTS

Examples on the left are also known as "Dyck words".

REFERENCE

https://en.wikipedia.org/wiki/Dyck_language

CROSSREFS

Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961

KEYWORD

easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable

CONCEPT recursion (info | search)

AUTHOR

Aaron David Fairbanks

BP961 Includes itself on the left vs. includes itself on the right.
(edit; present; nest [left/right]; search; history)
COMMENTS

Some examples are Bongard Problems with this solution.

CROSSREFS

Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960  *  BP962 BP963 BP964 BP965 BP966

KEYWORD

nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

AUTHOR

Aaron David Fairbanks

BP962 White vs. black.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP957 BP958 BP959 BP960 BP961  *  BP963 BP964 BP965 BP966 BP967

KEYWORD

precise, allsorted, minimal, dual, blackwhite, gap, left-finite, right-finite, left-full, right-full, left-null, finished, preciseworld, unstableworld

WORLD

[smaller | same | bigger]
zoom in left (blank_image) | zoom in right (black_image)

AUTHOR

Leo Crabbe

BP965 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.
(edit; present; nest [left/right]; search; history)
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

BP971 Left half has more black (less white) than right half versus vice versa.
(edit; present; nest [left/right]; search; history)
COMMENTS

A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half."

CROSSREFS

See BP972 for the version with examples rotated a quarter-turn.

Adjacent-numbered pages:
BP966 BP967 BP968 BP969 BP970  *  BP972 BP973 BP974 BP975 BP976

KEYWORD

nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent

AUTHOR

Aaron David Fairbanks

BP972 Top half has more black (less white) than bottom half versus vice versa.
(edit; present; nest [left/right]; search; history)
COMMENTS

A similar, but different, solution is "center of mass is above the horizontal vs. center of mass is below the horizontal."

CROSSREFS

See BP971 for the version with examples rotated a quarter-turn.

Adjacent-numbered pages:
BP967 BP968 BP969 BP970 BP971  *  BP973 BP974 BP975 BP976 BP977

KEYWORD

precise, spectrum, dual, handed, updown, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent

AUTHOR

Aaron David Fairbanks

BP977 Two of the same object are enclosed in the same space (there is a path between them) vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

An "object" is everything within some black boundary.

CROSSREFS

See BP1071 for a version with only squares and with infinite nesting allowed.

Adjacent-numbered pages:
BP972 BP973 BP974 BP975 BP976  *  BP978 BP979 BP980 BP981 BP982

KEYWORD

nice, precise, allsorted, creativeexamples, traditional

CONCEPT separated_regions (info | search),
identical (info | search),
recursion (info | search),
imagined_line_or_curve (info | search),
same_shape (info | search),
same (info | search)

AUTHOR

Aaron David Fairbanks

BP986 Palindromes vs. not palindromes.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."

CROSSREFS

Adjacent-numbered pages:
BP981 BP982 BP983 BP984 BP985  *  BP987 BP988 BP989 BP990 BP991

KEYWORD

nice, precise, allsorted, notso, sequence, traditional

CONCEPT element_wise_symmetry (info | search),
identical (info | search),
sequence (info | search),
same_shape (info | search),
same (info | search),
symmetry (info | search)

WORLD

zoom in left | zoom in right

AUTHOR

Jago Collins

BP988 Number of dots is a power of 2 vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Numbers of dots on the left can be obtained by repeatedly doubling 1 dot.

Numbers of dots on the left are the number of corners of a cube in some dimension.

CROSSREFS

Adjacent-numbered pages:
BP983 BP984 BP985 BP986 BP987  *  BP989 BP990 BP991 BP992 BP993

KEYWORD

stub, precise, allsorted, number, left-narrow, right-null, help, preciseworld

WORLD

dots [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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