All examples are Bongard Problems fitting left in BP954.

This is very close to BP927, specialized to Bongard Problems fitting left in BP954. The difference is that a Bongard Problem solution would fit left in BP927 but right here if it can sort images of it on both sides, but it is impossible to make an image of it fractally including itself on a certain side. An example is EX7997.

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

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, which 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, abstract, creativeexamples, left-narrow, rules, miniworlds

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

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

Adjacent-numbered pages:
BP1044 BP1045 BP1046 BP1047 BP1048  *  BP1050 BP1051 BP1052 BP1053 BP1054

teach, creativeexamples, left-narrow, right-narrow, contributepairs, fixedgrid, miniworlds

Jago Collins

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

Other ways of phrasing this:

"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.

The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.

Adjacent-numbered pages:
BP1122 BP1123 BP1124 BP1125 BP1126  *  BP1128 BP1129 BP1130 BP1131 BP1132

abstract, creativeexamples, left-unknowable, rules, miniworlds

[smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1150 BP1151 BP1152 BP1153 BP1154  *  BP1156 BP1157 BP1158 BP1159 BP1160

abstract, unwordable, creativeexamples, right-unknowable, traditional, finishedexamples, rules

Leo Crabbe

Adjacent-numbered pages:
BP1156 BP1157 BP1158 BP1159 BP1160  *  BP1162 BP1163 BP1164 BP1165 BP1166

unwordable, notso, arbitrary, handed, leftright, updown, stretch, blackwhite, creativeexamples, right-null, perfect, pixelperfect, help

Leo Crabbe

Jago originally designed this as a triptych. EX9655, EX9656, and EX9657 belong in a third category displayed further right of the two categories shown here. The third category is "all possible ways of matching are equally natural". - Aaron David Fairbanks, Apr 18 2022

Adjacent-numbered pages:
BP1186 BP1187 BP1188 BP1189 BP1190  *  BP1192 BP1193 BP1194 BP1195 BP1196

nice, abstract, creativeexamples, structure, miniworlds, dithering

Jago Collins