Fractal Crown

Fractal Crown – as described on Paul Bourke’s web site, equations by Roger Bagula

(* runtime: 10 seconds *)
n = 275; a = 5.0; b = Log[2]/Log[3]; image = Table[0, {n}, {n}];
Do[w = Sum[E^(I (-a)^k t)/a^(b k), {k, 1, 14}]; {i, j} = Floor[n({Re[w], Im[w]}/1.25 + 0.5)]; image[[i, j]] = Abs[w], {t, -Pi, Pi, 0.001}];
ListDensityPlot[image, Mesh -> False, Frame -> False];

This is how you can make this fractal in POV-Ray:
// runtime: 2 seconds
camera{location <0,0,1.25> look_at 0}
#macro Exp(Z) exp(Z.x)* #end
#declare a=5; #declare b=ln(2)/ln(3); #declare t1=-pi;
#while(t1<=14) #declare w=w+Exp(<0,1>*pow(-a,k)*t1)/pow(a,b*k); #declare k=k+1; #end sphere{w,0.003 pigment{rgb vlength(w)} finish{ambient 1}} #declare t1=t1+0.001; #end


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