There's also a possible intermediate case, where as the finite stages approach the limiting fractal in question, there *is* self-identification in the limit, yet the limiting fractal is nevertheless a simple closed curve. (E.g., in the way that identifying each x in [1,2] in the reals R with both y(x) = 2-x in [0,1], and z(x) = 4-x in [2,3], leads to a quotient space that is still topologically equivalent to R.) --Dan I wrote: << For this fractal, of dimension = log_5(9), it's not immediately obvious to me that it is a simple closed curve. Each of the finite stages that approach the limit is indeed a simple closed curve, but it seems possible that the limiting process might lead to some self-identification. I'd probably lean towards betting that it's *not* a simple closed curve. Anyone know the answer?

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele