An Algorithm for computing the Filled Julia Set of Qc(z)

Choose a complex number, x0 + y0i, and the parameter
c = c0 + c1i.


for m = 1 to 300
   for n = 1 to 300
      iterate x0 + y0i up to 20 times
      if, at any point, we exceed 4,
         color the pixel (n,m)
         some color
      if, after 20 iterations, 
      we have not exceeded 4, then
         color the pixel (n,m) black
   end for
end for

Notes:

This algorithm is not foolproof. It is impossible for any computer to determine whether or not an orbit is bounded in a finite amount of time.

Since we are choosing an artificial infinity, the number of iterations may affect the colors.