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 considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and ignoring pixelation), as a panel.

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

Leo Crabbe

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

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 "infodense" on the OEBP.

Consider the amount of data a person has to consciously unpack in each example in the process of determining how it should be sorted. In BP3, it is only necessary to notice the color of the shape. In BP871, however, it is important to read various qualities of every tiny shape shown.

Images of Bongard Problems that are "infodense" typically need to include a large number of examples in order to communicate the solution clearly without admitting unintended solutions. With so much data packed in each example, it becomes more likely that some of the random patterns in the data will happen to distinguish between the two sides in an unintended way. A similar issue appears in convoluted Bongard Problems.

Contrast "infodense" Problems to hardsort Bongard Problems, in which examples are difficult to sort, but perhaps that difficulty does not stem from reading a high amount of information; perhaps there is a small amount of information extracted from the examples, but it is hard to determine whether or not that information fits a rule.

Adjacent-numbered pages:
BP973 BP974 BP975 BP976 BP977  *  BP979 BP980 BP981 BP982 BP983

abstract, spectrum, meta (see left/right), links, keyword

Aaron David Fairbanks

All examples in this Problem are images of Bongard Problems that would fit left in BP954.

Adjacent-numbered pages:
BP982 BP983 BP984 BP985 BP986  *  BP988 BP989 BP990 BP991 BP992

abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant, visualimagination

Leo Crabbe

Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)

See BP793 and BP1004 for similar paradoxes.

See BP1005 for the version about only numerical properties; examples in that BP would be sorted the same way here that they are there.

See BP1003 for a similar idea. Rather than the collection of collections imitating the individual collections, BP1003 is about the total combined collection imitating the individual collections. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.

Also see BP1004, is likewise about the whole satisfying the same rule as its parts, but there the parts don't themselves have to be collections; there the parts are just plain individual objects. The panels in BP999 (this BP) should be sorted the same way in BP1004.

See BP1002, which is about only visual self-similarity instead of more general conceptual "self-similarity".

Adjacent-numbered pages:
BP994 BP995 BP996 BP997 BP998  *  BP1000 BP1001 BP1002 BP1003 BP1004

nice, stub, abstract, creativeexamples, left-narrow, rules, miniworlds

[smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

See BP1004 for a Problem about conceptual self-similarity instead of visual self-similarity.

See BP188 for a similar Problem restricted to shape outlines made of shape outlines.

Adjacent-numbered pages:
BP997 BP998 BP999 BP1000 BP1001  *  BP1003 BP1004 BP1005 BP1006 BP1007

easy, nice, fuzzy, abstract, anticomputer, concept, traditional

Aaron David Fairbanks

Since it is most intuitive to imagine spatially squishing together all the collections in the process of combining them into one big collection, avoid rules that involve relative spatial positionings of objects.

Contrast BP999, which is very similar. There, when considering the whole picture, the collections are to be treated as individual objects; here, when considering the whole picture, the collections are to be combined into one big collection. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.

Also contrast BP1004, which is about a collection of plain objects obeying the same rule as all the objects (instead of a collection of [collections of objects] obeying the same rule as all the [collections of objects]).

See BP1006 for the version with only number-based properties. All panels in that Bongard Problem fit the same way in this Bongard Problem as well.

Adjacent-numbered pages:
BP998 BP999 BP1000 BP1001 BP1002  *  BP1004 BP1005 BP1006 BP1007 BP1008

nice, abstract, notso, creativeexamples, rules, miniworlds

[smaller | same | bigger]

Leo Crabbe, Aaron David Fairbanks

The "whole" is the entire panel including the bounding box. A "part" is some region either stylistically different or amply separated in space from everything else. Smaller parts-within-parts don't count as parts.

Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)

See BP793 and BP999 for similar paradoxes.

See BP1006 for the version about numerical properties where each part is a cluster of dots; examples in that BP would be sorted the same way here that they are there.

See BP999 and BP1003 for versions where each object is itself a collection of objects, so that the focus is on rules specifically pertaining to collections (e.g. "all the objects are different").

See BP1002 for a Bongard Problem about only visual self-similarity instead of conceptual self-similarity.

The rule shown in each panel is "narrow" (see BP513^left and BP514^left).

Adjacent-numbered pages:
BP999 BP1000 BP1001 BP1002 BP1003  *  BP1005 BP1006 BP1007 BP1008 BP1009

nice, abstract, anticomputer, creativeexamples, left-narrow, rules, miniworlds

Aaron David Fairbanks

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

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

This is a special case of BP841 and a generalisation of BP822.

Adjacent-numbered pages:
BP1105 BP1106 BP1107 BP1108 BP1109  *  BP1111 BP1112 BP1113 BP1114 BP1115

nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering

Leo Crabbe