Bongard Problems sorted left have the keyword "meta" on the OEBP.

Meta Bongard Problems are Bongard Problems that sort Bongard Problems. Sometimes abbreviated MBPs.

The first meta Bongard Problem was BP200.

Some meta BP pages sort images of Bongard Problems (keyword miniproblems), while other meta BP pages sort other BP pages (keyword links).

BPs that sort meta-BPs are labelled metameta.

Adjacent-numbered pages:
BP532 BP533 BP534 BP535 BP536  *  BP538 BP539 BP540 BP541 BP542

meta (see left/right), links, keyword, world, left-self, sideless, metameta, left-full, feedback

bp [smaller | same | bigger]
zoom in left (linksbp)

Aaron David Fairbanks

Adjacent-numbered pages:
BP533 BP534 BP535 BP536 BP537  *  BP539 BP540 BP541 BP542 BP543

less, notso, left-finite, finished, invalid, experimental, funny

Aaron David Fairbanks

This Problem admits multiple solutions besides "Solution for this problem in English text vs. not so," some of which are listed as the left examples. Some do not depend on the English language, so this Problem is technically "solvable" without the relevant cultural information.

Adjacent-numbered pages:
BP540 BP541 BP542 BP543 BP544  *  BP546 BP547 BP548 BP549 BP550

less, notso, culture, finished, invalid, experimental, funny

Aaron David Fairbanks

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

These are meta Bongard Problems with at least two layers of nesting.

See BP952 for the version that sorts pictures of Bongard Problems (miniproblems) instead of links.

Adjacent-numbered pages:
BP542 BP543 BP544 BP545 BP546  *  BP548 BP549 BP550 BP551 BP552

meta (see left/right), links, keyword, left-self, metameta, metametameta, left-it, feedback

bp [smaller | same | bigger]
zoom in left (metametabp)

Aaron David Fairbanks

Right examples have the keyword "wellfounded" on the OEBP.

This BP is not wellfounded, but its right side is. A paradoxical BP would be "Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems on the right side vs. this can never happen": where does it sort itself?

left-self or right-self implies not wellfounded.

Wellfounded implies not feedback.

Adjacent-numbered pages:
BP789 BP790 BP791 BP792 BP793  *  BP795 BP796 BP797 BP798 BP799

meta (see left/right), links, keyword, left-self, metameta, left-it, feedback

linksbp [smaller | same | bigger]

Aaron David Fairbanks

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

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 BP953, BP902.

Adjacent-numbered pages:
BP954 BP955 BP956 BP957 BP958  *  BP960 BP961 BP962 BP963 BP964

meta (see left/right), miniproblems, left-finite, right-finite, left-full, right-full, right-null, perfect, infinitedetail, finished, experimental, funny

zoom in left | zoom in right (blank_image)

Aaron David Fairbanks, Leo Crabbe