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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. |
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COMMENTS
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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. |
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CROSSREFS
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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
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KEYWORD
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hard, precise, distractingworld, perfect
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CONCEPT
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local_global (info | search)
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AUTHOR
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Aaron David Fairbanks
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CROSSREFS
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Adjacent-numbered pages:
BP957 BP958 BP959 BP960 BP961  *  BP963 BP964 BP965 BP966 BP967
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KEYWORD
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precise, allsorted, minimal, dual, blackwhite, gap, left-finite, right-finite, left-full, right-full, left-null, finished, preciseworld, unstableworld
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WORLD
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[smaller | same | bigger] zoom in left (blank_image) | zoom in right (black_image)
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AUTHOR
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Leo Crabbe
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BP961 |
| Includes itself on the left vs. includes itself on the right. |
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COMMENTS
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Some examples are Bongard Problems with this solution. |
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CROSSREFS
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Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960  *  BP962 BP963 BP964 BP965 BP966
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KEYWORD
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nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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AUTHOR
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Aaron David Fairbanks
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BP956 |
| Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets). |
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COMMENTS
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Examples on the left are also known as "Dyck words". |
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REFERENCE
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https://en.wikipedia.org/wiki/Dyck_language |
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CROSSREFS
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Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961
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KEYWORD
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easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable
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CONCEPT
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recursion (info | search)
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AUTHOR
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Aaron David Fairbanks
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BP951 |
| Process described leaves some inputs invariant vs. no output will resemble its input. |
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COMMENTS
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There are many ambiguities here. The solver is expected to determine what things are "allowed" to be inputs for each process. To avoid confusion examples should not be sorted differently if you consider inputting nothing.
In each example there is at least some overlap between the set of possible inputs and the set of possible outputs for each process. If we did not apply this constraint, an easy example to be sorted right would be a process that turns blue shapes red.
A harder-to-read but more clearly defined version of this Problem could include within each example a mini Bongard Problem sorting left all allowed inputs for the process. |
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REFERENCE
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https://en.wikipedia.org/wiki/Fixed_point_(mathematics) |
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CROSSREFS
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Adjacent-numbered pages:
BP946 BP947 BP948 BP949 BP950  *  BP952 BP953 BP954 BP955 BP956
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KEYWORD
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structure, rules, miniworlds
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CONCEPT
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function (info | search)
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AUTHOR
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Leo Crabbe
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BP949 |
| Two unique distances between points vs. three unique distances between points. |
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BP946 |
| Can be constructed using 2 identical copies of an image (full overlapping not allowed) vs. not so. |
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COMMENTS
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"Full overlapping not allowed" means you cannot overlay an image onto itself without moving it; if this were allowed all images would be sorted on the left. The copies can be moved around (translated) in 2D but can not be flipped or rotated.
There are examples on the right drawn with thick lines, and these could be created by copying an image with slightly thinner lines and moving it over a tiny amount. If you fix this issue by saying "the copy has to be moved over more than a tiny amount" then the Bongard Problem is perfect but not precise, but if you fix this issue by saying "interpret the figures as made up of (infinitesimally) thin lines" then it's precise but not perfect. - Aaron David Fairbanks, Jun 17 2023 |
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CROSSREFS
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Adjacent-numbered pages:
BP941 BP942 BP943 BP944 BP945  *  BP947 BP948 BP949 BP950 BP951
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KEYWORD
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nice, notso, creativeexamples
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AUTHOR
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Leo Crabbe
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BP945 |
| Cube number of dots vs. non-cube number of dots. |
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