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BP1116 Contains self somewhere within any area around any point within self vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".


The left hand side of this is a weaker condition than the left hand side of BP1241.

CROSSREFS

Adjacent-numbered pages:
BP1111 BP1112 BP1113 BP1114 BP1115  *  BP1117 BP1118 BP1119 BP1120 BP1121

KEYWORD

notso, perfect, infinitedetail

CONCEPT topological_density (info | search),
fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

connected_fractal [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1241 Any point contained in (arbitrarily) smaller version of self vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

notso, perfect, infinitedetail

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

connected_fractal [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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