Search: ex:EX9055
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BP532 |
| Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself. |
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BP1116 |
| Contains self somewhere within any area around any point within self vs. not so. |
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BP1119 |
| Tiled by finitely many smaller copies of itself (different sizes allowed) vs. not so. |
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BP1120 |
| No same-sized copies of self overlap vs. distinct same-sized copies overlap. |
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BP1239 |
| Fractal topologically closed (each white point has a neighborhood of pure white surrounding it) vs. not |
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BP1241 |
| Any point contained in (arbitrarily) smaller version of self vs. not so. |
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COMMENTS
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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. |
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CROSSREFS
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Adjacent-numbered pages:
BP1236 BP1237 BP1238 BP1239 BP1240  *  BP1242 BP1243 BP1244 BP1245 BP1246
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KEYWORD
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notso, perfect, infinitedetail
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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WORLD
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connected_fractal [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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