Yes, if you let T_k, k in Z/4Z denote the transformation C -> C of the form z |-> az+b. a,b in C, that takes [0,1] to the kth segment of the initial "witch's hat" stage of the snowflake (4 intervals of length 1/3 each), then a parametrization S: [0,1] -> C of the snowflake curve should satisfy S({t}) = T_[4t](S(t)) (where {} is fractional part and [] is floor). Does this determine S uniquely? --Dan Rich wrote: << If you view the starting triangle as running from 0 to 3, and write the fraction base 4, you can use the fraction digits to select which part of the (sub)edge you are on. The orientation of the edge can be calculated from the 1s and 2s of the high order portion of the fraction, and that should give a somewhat kludgy sum for the (x,y) coordinates of the image point. RWG likely has some nice FFT clock sum expression

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