This must be one of those puzzles that RWG posts already knowing the answer, because a couple of drawings immediately gives it. Answer given below, under thirty blank lines in case others want to solve it. D = 2 log 3 / log 5 ~ 1.36521+ On Tue, Jun 23, 2009 at 11:35 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Thanks, Alan.
So, does this make it the same as starting with a plus sign of 5 adjacent squares, and taking 5 congruent copies snuggled together and normalized -- then iterate to the limit? (Actually the boundary of this limit.)
If so, it's a fractal I was studying just a couple of months ago. I'll go review what I had about it.
=-Dan
<< I'm pretty sure I understand the intended construction. We'll construct a sequence of sets of complex numbers; the limit of this sequence will be (well-defined and) the intended fractal.
Let Q[0] contain only 0. Then for any nonnegative integer i, let Q[i+1] = (Q[i] + {0, 1, -1, i, -i}) / (2i + 1). Here, if A and B are sets, the set A+B is intended to mean {a+b | a in A and b in B}.
Each Q is roughly cross-shaped; RWG observes (very tersely) that dividing by 2i+1 rotates and shrinks each such cross by just enough that five crosses can snuggle together to make a meta-cross.
I think this fractal is in Mandelbrot; I cannot dig up my copy at the moment.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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