Adjacent-numbered pages:
BP944 BP945 BP946 BP947 BP948  *  BP950 BP951 BP952 BP953 BP954

nice, precise, allsorted, stretch, perfect, traditional, preciseworld

3_or_4_points [smaller | same | bigger]

Leo Crabbe

Left-sorted Bongard Problems have the keyword "arbitrary" on the OEBP.

Arbitrary BPs often communicate non-arbitrary ideas. M. M. Bongard's original "A vs. Б" Problem (BP100) is about recognizing letters. A choice of some such arbitrary letters was necessary.

Most Bongard Problems are at least slightly arbitrary. Almost any Bongard Problem could be changed in a number of ways to make slightly different Bongard Problems. When a Bongard Problem is labeled as "arbitrary", that means there is one especially obvious class of similar Bongard Problems, with none of them particularly more interesting or special than any other.

The self-referential (invalid) Bongard Problems BP538, BP545, BP902, BP1073 fit this definition (the solution involves the arbitrary detail of being that specific Bongard Problem instead of any other). On the other hand, the solution idea is not arbitrary when phrased with "this Bongard Problem".

Many "arbitrary" Bongard Problems are of the form "Detail X has arbitrary value A vs. not so" or "Detail X has arbitrary value A vs. detail X has arbitrary value B". Other "arbitrary" Bongard Problems feature arbitrary details that are not the distinction between the sides, e.g. BP545.

It is unclear whether or not we should label a Bongard Problem "arbitrary" if the arbitrarily fixed detail is a notable special case. For example, BP1024 could have been made using any number, but the number 1 is a non-arbitrary number, so the Bongard Problem does not seem so arbitrary.

Similar to thespecificity concept BP (BP773), which is more general, including Bongard Problems relating conceptually in any way to arbitrary specificity.

Adjacent-numbered pages:
BP945 BP946 BP947 BP948 BP949  *  BP951 BP952 BP953 BP954 BP955

meta (see left/right), links, keyword, right-self, sideless

bp [smaller | same | bigger]

Aaron David Fairbanks

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.

https://en.wikipedia.org/wiki/Fixed_point_(mathematics)

Adjacent-numbered pages:
BP946 BP947 BP948 BP949 BP950  *  BP952 BP953 BP954 BP955 BP956

structure, rules, miniworlds

Leo Crabbe

See BP547 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Any left example in this BP will be a left example for BP1084.

Adjacent-numbered pages:
BP947 BP948 BP949 BP950 BP951  *  BP953 BP954 BP955 BP956 BP957

meta (see left/right), miniproblems, funny, presentationinvariant

[smaller | same | bigger]
zoom in left

Leo Crabbe

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

See BP959, BP902.

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

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

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

Leo Crabbe

Loosely speaking, examples on the left are "Bongard Problems that can be self-similar". However, Bongard Problems with images of themselves deeply nested in boxes or rotated/flipped are not here considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and allowing infinite detail, ignoring pixelation--see keyword infinitedetail), as a panel.

Bongard Problems fitting left evidently come in three categories: 1) the Bongard Problem could only appear on its own left side, 2) the Bongard Problem could appear on its own right side, or 3) the Bongard Problem could appear on its own left or the right side. See BP987.

Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit left here.

All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side. (A more general version of this Bongard Problem might allow many formats of Bongard Problems, sorting an image left if a self-similar version is possible having the same solution and format. This more general version would no longer be tagged presentationinvariant, since sorting would not only depend on solution, but also format.)

It would hint at the solution (keyword help) to only include images of Bongard Problems that, as it stands, are already clearly categorized on one side by themselves. (That is, images of Bongard Problems that belong on one of the two sides of BP793.) It is tricky to come up with images that are categorized by themselves as it stands but that could NOT be recursively included within themselves. EX7967, EX7999, EX7995, and EX6574 are some examples.

See BP987 which narrows down the left-hand side of this BP further based on whether or not the BP could contain itself as a panel on both sides.

Adjacent-numbered pages:
BP949 BP950 BP951 BP952 BP953  *  BP955 BP956 BP957 BP958 BP959

hard, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination

Leo Crabbe

See also BP957 for the other two evident possibilities.

Adjacent-numbered pages:
BP950 BP951 BP952 BP953 BP954  *  BP956 BP957 BP958 BP959 BP960

abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental

oblong_boxes_bpimage_sorts_both_sides_skewed [smaller | same | bigger]
zoom in left (oblong_boxes_bpimage_sorts_both_sides_left) | zoom in right (oblong_boxes_bpimage_sorts_both_sides_right)

Leo Crabbe

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

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

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

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

Aaron David Fairbanks

See also BP955 for the other two evident possibilities.

Adjacent-numbered pages:
BP952 BP953 BP954 BP955 BP956  *  BP958 BP959 BP960 BP961 BP962

nice, abstract, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental

oblong_panels_bpimage_sorts_both_sides_balanced [smaller | same | bigger]
zoom in left (oblong_panels_bpimage_sorts_both_sides_stay) | zoom in right (oblong_panels_bpimage_sorts_both_sides_swap)

Leo Crabbe

Left examples have the keyword "infinitedetail" on the OEBP.

Image files on the OEBP do not really have infinite detail. For a panel to be intuitively read as having infinite detail, there usually needs to be some apparent self-similarity, or perhaps a sequence of objects following an easy to read pattern getting smaller and smaller with increasing pixelation.

Usually in "infinitedetail" Bongard Problems, not only is it a puzzle to figure out the solution, but it is another puzzle to find self-similarities and understand the intended infinite detail in each example.

BPs tagged with the keyword "infinitedetail" usually feature pixelated images that give the closest approximation of the intended infinite structure up to pixelation. This means they should be tagged with the keyword perfect, but should not be tagged with the keyword pixelperfect.

Just because a Bongard Problem has "infinitedetail" does not necessarily make it infodense. Some fractal images might be encoded by a small amount of information (just the information about which places within itself it includes smaller copies of itself) and may be recognized quickly.

Adjacent-numbered pages:
BP953 BP954 BP955 BP956 BP957  *  BP959 BP960 BP961 BP962 BP963

notso, meta (see left/right), links, keyword, wellfounded

visualbp [smaller | same | bigger]

Aaron David Fairbanks