Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.

Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.

See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.

Adjacent-numbered pages:
BP960 BP961 BP962 BP963 BP964  *  BP966 BP967 BP968 BP969 BP970

hard, precise, distractingworld, perfect

Aaron David Fairbanks

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

In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.

See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.

Adjacent-numbered pages:
BP1241 BP1242 BP1243 BP1244 BP1245  *  BP1247 BP1248 BP1249 BP1250 BP1251

precise, allsorted, unwordable, notso, traditional

Aaron David Fairbanks

"Local vs. global."

For clarity, rules involving diagonal neighbors or squares more than one step away are never used.

The similar solution "Each square can be deduced from its neighbors vs. not so" does not quite work; for example EX8114 would then not fit left. See also BP1258 ("Each square can be deduced from the rest vs. not so").

Adjacent-numbered pages:
BP1252 BP1253 BP1254 BP1255 BP1256  *  BP1258 BP1259 BP1260 BP1261 BP1262

structure, rules, grid, miniworlds

grid_of_images_with_rule [smaller | same | bigger]

Aaron David Fairbanks