24 Oct
2016
24 Oct
'16
11:47 a.m.
Howard Cannon used Julian's fractal Fourier expander to make gosper.org/mandelfou.png illustrating that it fills some areas unboundedly faster than others. (dArea/dt is interesting.) The function has no symmetry, i.e., for no (nontrivial) a, b does Z(t) = a(Z(b(t)), and there is no symmetry in the filled areas of winding number 1 of the Fourier approximations, such as illustrated. (Except for the fundamental circle and ellipse. gosper.org/mandelfou-1-2-3.png) Yet for infinitely many discrete samplings, the filled (polygonal) area does have symmetry, e.g, gosper.org/blusno.gif . --rwg