BP1206 is the same solution but using the vertical axis instead of the horizontal axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1202 BP1203 BP1204 BP1205 BP1206  *  BP1208 BP1209 BP1210 BP1211 BP1212

stub, notso, stretch, left-narrow, traditional

Aaron David Fairbanks

The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".

BP1207 is the same solution but using the horizontal axis instead of the vertical axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1201 BP1202 BP1203 BP1204 BP1205  *  BP1207 BP1208 BP1209 BP1210 BP1211

stub, notso, stretch, left-narrow, traditional

Aaron David Fairbanks

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.

See unstable vs. stable for changing content within a small area.

Adjacent-numbered pages:
BP1200 BP1201 BP1202 BP1203 BP1204  *  BP1206 BP1207 BP1208 BP1209 BP1210

meta (see left/right), links, keyword, stability

Aaron David Fairbanks

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".

Adjacent-numbered pages:
BP1199 BP1200 BP1201 BP1202 BP1203  *  BP1205 BP1206 BP1207 BP1208 BP1209

meta (see left/right), links, keyword

Aaron David Fairbanks

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.

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

meta (see left/right), links, keyword

Aaron David Fairbanks

See BP1199 for the version with rectangles.

Adjacent-numbered pages:
BP1196 BP1197 BP1198 BP1199 BP1200  *  BP1202 BP1203 BP1204 BP1205 BP1206

precise, traditional, left-listable, right-listable

Aaron David Fairbanks

Another wording: "can be repeatedly broken along 'fault lines' to yield individual pieces vs not."

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.

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

hard, precise, challenge, proofsrequired, inductivedefinition, left-listable, right-listable

Aaron David Fairbanks

All of the examples fitting left here would fit right in BP1200 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

All of the examples fitting left in BP1097 (re-styled) would fit right here (besides the two possible arrangements made up of just two rectangles, but those aren't shown there).

See BP1201 for the version with triangles.

Adjacent-numbered pages:
BP1194 BP1195 BP1196 BP1197 BP1198  *  BP1200 BP1201 BP1202 BP1203 BP1204

precise, traditional, left-listable, right-listable

Aaron David Fairbanks

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

Bongard's original Problems never involved shades of gray. They were just black and white drawings.

Adjacent-numbered pages:
BP1193 BP1194 BP1195 BP1196 BP1197  *  BP1199 BP1200 BP1201 BP1202 BP1203

meta (see left/right), links, keyword

Aaron David Fairbanks

https://en.wikipedia.org/wiki/Square-free_word

Adjacent-numbered pages:
BP1192 BP1193 BP1194 BP1195 BP1196  *  BP1198 BP1199 BP1200 BP1201 BP1202

precise, allsorted, notso, left-narrow, sequence, traditional, preciseworld, dithering, left-listable

Aaron David Fairbanks