/*

  Mandelbrot set in Picat.

  See 
   * http://en.wikipedia.org/w/index.php?title=Mandelbrot_set
   * http://rosettacode.org/wiki/Mandelbrot_set

  This solution was inspired by the Icon/Unicon version:
    http://rosettacode.org/wiki/Mandelbrot_set#Icon_and_Unicon


  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

main => go.

go => 

   Width = 90,
   Height = 50,
   Limit = 50,
   foreach(Y in 1..Height)
      P="",
      foreach (X in 1..Width) 
         Z=complex(0,0),
         C=complex(2.5*X/Width-2.0,2.0*Y/Height-1.0),
         J = 0,
         while (J < Limit, c_abs(Z)<2.0) 
            Z := c_add(c_mul(Z,Z),C),
            J := J + 1
         end,
         if J == Limit then
             P := P ++ "#"
         else 
             P := P ++ "."
         end
      end,
      printf("%s\n", P)
  end,
  nl.


complex(R,I) = [R,I].
c_add(X,Y) = complex(X[1]+Y[1],X[2]+Y[2]).
c_mul(X,Y) = complex(X[1]*Y[1]-X[2]*Y[2],X[1]*Y[2]+X[2]*Y[1]).
c_abs(X) = sqrt(X[1]*X[1]+X[2]*X[2]).