# Mandelbrot Set

Mathematically, the Mandelbrot set is defined on the plane of complex numbers

//Function

def mandelbrot(wd,ht,mx)

{

return [Imperative]

{

it = [];

for (rw in 0..ht-1)

{

for (cl in 0..wd-1)

{

rl = (cl - wd/2.0)*4.0/wd;

im = (rw - ht/2.0)*4.0/wd;

x = 0;

y = 0;

n = 0;

while (x*x+y*y <= 4 && n < mx)

{

x1 = x*x - y*y + rl;

y = 2*x*y + im;

x = x1;

n = n + 1;

}

it[cl][rw] = n;

}

}

return it;

}

};

wd = 200;

hg = 200;

m = mandelbrot(wd,hg,50);

//Visualization

q = List.Reverse(List.Sort(List.UniqueItems(List.Flatten(m,-1))));

r = List.DropItems(Math.Round(Math.RemapRange(q,10,250)),-1);

d = Dictionary.ByKeysValues(q+"", List.Flatten([Color.ByARGB

(250,175,230,125),Color.ByARGB(List.Reverse(r),List.ShiftIndices

(r,100),List.ShiftIndices(r,-13),List.Reverse(r))],-1));

c = Image.FromPixels(List.Transpose(d.ValueAtKey(m+"")));

//Surface

pt1 = Point.ByCoordinates((-wd/2..wd/2..#wd)<1>,(-hg/2..hg/2..#hg)<2>);

el1 = List.Chop(Math.RemapRange(List.Flatten(m,-1),0,hg/10),hg);

sr1 = NurbsSurface.ByControlPoints(pt1.Translate(Vector.ZAxis(),el1));

sr2 = GeometryColor.BySurfaceColors(sr1,d.ValueAtKey(m+""));

Maximum Iterations: 10

Maximum Iterations: 30

Joni "Let’s draw the Mandelbrot set!", November 17, 2013 <https://jonisalonen.com/2013/lets-draw-the-mandelbrot-set/> January 26, 2021

Last modified 2yr ago