Mandelbrot set

You are encouraged to solve this task according to the task description, using any language you may know.


Task

Generate and draw the Mandelbrot set.



Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .




with Lumen.Binary;
package body Mandelbrot is
   function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor is
      use type Lumen.Binary.Byte;
      Result : Lumen.Image.Descriptor;
      X0, Y0 : Float;
      X, Y, Xtemp : Float;
      Iteration   : Float;
      Max_Iteration : constant Float := 1000.0;
      Color : Lumen.Binary.Byte;
   begin
      Result.Width := Width;
      Result.Height := Height;
      Result.Complete := True;
      Result.Values := new Lumen.Image.Pixel_Matrix (1 .. Width, 1 .. Height);
      for Screen_X in 1 .. Width loop
         for Screen_Y in 1 .. Height loop
            X0 := -2.5 + (3.5 / Float (Width) * Float (Screen_X));
            Y0 := -1.0 + (2.0 / Float (Height) * Float (Screen_Y));
            X := 0.0;
            Y := 0.0;
            Iteration := 0.0;
            while X * X + Y * Y <= 4.0 and then Iteration < Max_Iteration loop
               Xtemp := X * X - Y * Y + X0;
               Y := 2.0 * X * Y + Y0;
               X := Xtemp;
               Iteration := Iteration + 1.0;
            end loop;
            if Iteration = Max_Iteration then
               Color := 255;
            else
               Color := 0;
            end if;
            Result.Values (Screen_X, Screen_Y) := (R => Color, G => Color, B => Color, A => 0);
         end loop;
      end loop;
      return Result;
   end Create_Image;
 
end Mandelbrot;