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| BP1199 |
| The only rectangles are the individual regions and the whole vs. there is some other rectangle made of rectangles. |
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| BP1200 |
| The whole rectangle can be filled in by successively replacing pairs of adjacent rectangles with one vs. not so. |
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COMMENTS
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Another wording: "can be repeatedly broken along 'fault lines' to yield individual pieces vs not." |
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REFERENCE
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Robert Dawson, A forbidden suborder characterization of binarily composable diagrams in double categories, Theory and Applications of Categories, Vol. 1, No. 7, p. 146-145, 1995. |
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CROSSREFS
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All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.
All of the examples fitting right in in BP1097 (re-styled) would fit right here (besides a single solid block, but that isn't shown there).
Adjacent-numbered pages:
BP1195 BP1196 BP1197 BP1198 BP1199 * BP1201 BP1202 BP1203 BP1204 BP1205
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KEYWORD
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hard, precise, challenge, proofsrequired, inductivedefinition, left-listable, right-listable
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AUTHOR
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Aaron David Fairbanks
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| BP1201 |
| The only triangles are the individual regions and the whole vs. there is some other triangle made of triangles. |
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| BP1202 |
| Color of any region is an equal mix of the colors of the overlapping shapes vs. not so. |
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| BP1203 |
| Bongard Problems where making a small change to some example makes it no longer fit in vs. Bongard Problems in which sufficiently small changes to examples keep them fitting in. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "unstableworld" on the OEBP.
Right-sorted Bongard Problems have the keyword "stableworld" on the OEBP.
In a "stableworld" Bongard Problem, no small change should outright make an example outright no longer fit in with the others in the Bongard Problem. It is allowed for a small change to make an example slightly less like all the others.
The meaning of "stableworld" is close to "examples have no particular format at all", but not quite the same. |
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CROSSREFS
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See unstable vs. stable, which is about examples switching sides upon small changes instead of being rendered unsortable.
See BP1144, which is about ALL small changes to ALL examples making them unsortable.
Adjacent-numbered pages:
BP1198 BP1199 BP1200 BP1201 BP1202 * BP1204 BP1205 BP1206 BP1207 BP1208
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KEYWORD
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meta (see left/right), links, keyword
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AUTHOR
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Aaron David Fairbanks
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| BP1204 |
| Meta Bongard Problems of the form "arbitrarily small [transformation] applied to some examples switch their sorting vs. the sorting of each example is invariant under sufficiently small applications of [transformation]" vs. other meta Bongard Problems. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "stability" on the OEBP.
For any "stability" Bongard Problem there could usually be made a corresponding invariance Bongard Problem ("[transformation] applied to some examples switch their sorting vs. sorting is invariant under [transformation]").
Potentially, "stability" Bongard Problems could be considered invariance Bongard Problems. On one hand, they are different, since checking whether arbitrarily small transformations switch an example's sorting is different from checking whether a particular transformation switches an example's sorting; the former is infinitely many conditions. On the other hand, there is actually only finitely much detail in any of the examples, and in practice a "stability" Bongard Problem generally just amounts to "a small application of [transformation] switches an example's sorting vs. not". |
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CROSSREFS
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Adjacent-numbered pages:
BP1199 BP1200 BP1201 BP1202 BP1203 * BP1205 BP1206 BP1207 BP1208 BP1209
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KEYWORD
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meta (see left/right), links, keyword
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AUTHOR
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Aaron David Fairbanks
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| BP1205 |
| Bongard Problems in which slight deformations (but perhaps across a large area) of examples can switch their sorting vs. Bongard Problems in which examples deformed slightly enough remain sorted the same way. |
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COMMENTS
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Left examples have the keyword "deformunstable" on the OEBP.
Right examples have the keyword "deformstable" on the OEBP.
For the purposes of this Bongard Problem, a "slight deformation" is a way of dragging the details of an image around which is relatively uniform in any local area and moves each point at most an arbitrarily small distance. More precise definitions could be made using mathematics.
In a "deformstable" Bongard Problem, no slight deformation should outright flip an example's sorting. It is allowed for a slight deformation to make an example sorted slightly more ambiguously. |
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CROSSREFS
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See unstable vs. stable for changing content within a small area.
Adjacent-numbered pages:
BP1200 BP1201 BP1202 BP1203 BP1204 * BP1206 BP1207 BP1208 BP1209 BP1210
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KEYWORD
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meta (see left/right), links, keyword, stability
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AUTHOR
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Aaron David Fairbanks
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| BP1206 |
| Vertical axis of symmetry vs. no vertical axis of symmetry. |
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