With mathematical jargon:

No distinct same-sized copies of self overlap on a subset with positive measure in the Hausdorff measure using the Hausdorff dimension.

For a covering of a fractal by finitely many scaled down copies of itself, the condition of that no two have an intersection with positive measure is equivalent to the condition that the Hausdorff dimension coincides with the similarity dimension.

(There is another similar condition in this context called the "open set condition" which implies this but is not equivalent. The open set condition is equivalent to the condition that the Hausdorff measure using the similarity dimension is nonzero.)

https://en.wikipedia.org/wiki/Hausdorff_dimension

https://en.wikipedia.org/wiki/Open_set_condition

Adjacent-numbered pages:
BP1115 BP1116 BP1117 BP1118 BP1119  *  BP1121 BP1122 BP1123 BP1124 BP1125

challenge, perfect, infinitedetail

[smaller | same | bigger]

Aaron David Fairbanks

Similar to BP818.

Adjacent-numbered pages:
BP1117 BP1118 BP1119 BP1120 BP1121  *  BP1123 BP1124 BP1125 BP1126 BP1127

nice, minimal, size, boundingbox, infinitedetail, preciseworld, absoluteposition

Leo Crabbe

This was created as an example of a Bongard Problem that could include an image of a Bongard Problem with the same solution as itself but could not include the very image of itself (appearing within itself fractally).

See also BP961, "appears on its own left side vs. appears on its own right side".

Adjacent-numbered pages:
BP1222 BP1223 BP1224 BP1225 BP1226  *  BP1228 BP1229 BP1230 BP1231 BP1232

stub, precise, allsorted, notso, handed, leftright, example, perfect, infinitedetail

Aaron David Fairbanks

Each example on the left is imagined to continue beyond the bounding box.

Adjacent-numbered pages:
BP1225 BP1226 BP1227 BP1228 BP1229  *  BP1231 BP1232 BP1233 BP1234 BP1235

stub, notso, perfect, infinitedetail, left-couldbe, bordercontent, blackwhiteinvariant

Aaron David Fairbanks

Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.

It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)

The left hand side of this is a stronger condition than the left hand side of BP1116.

Adjacent-numbered pages:
BP1236 BP1237 BP1238 BP1239 BP1240  *  BP1242 BP1243 BP1244 BP1245 BP1246

notso, perfect, infinitedetail

connected_fractal [smaller | same | bigger]

Aaron David Fairbanks