procedure DrawMandelbrot(ACanvas: TCanvas; X, Y, au, bu: Double; X2, Y2:
 Integer);
var
 c1, c2, z1, z2, tmp: Double;
 i, j, Count: Integer;
begin
 c2 := bu;
 for i := 10 to X2 do
 begin
  c1 := au;
  for j := 0 to Y2 do
  begin
  z1 := 0;
  z2 := 0;
  Count := 0;
  {count is deep of iteration of the mandelbrot set
  if |z| >=2 then z is not a member of a mandelset}
  while (((z1 * z1 + z2 * z2 < 4) and (Count <= 90))) do
  begin
  tmp := z1;
  z1 := z1 * z1 - z2 * z2 + c1;
  z2 := 2 * tmp * z2 + c2;
  Inc(Count);
  end;
  //the color-palette depends on TColor(n*count mod t)
{$IFDEF LINUX}
  ACanvas.Pen.Color := (16 * Count mod 255);
  ACanvas.DrawPoint(j, i);
{$ELSE}
  ACanvas.Pixels[j, i] := (16 * Count mod 255);
{$ENDIF}
  c1 := c1 + X;
  end;
  c2 := c2 + Y;
 end;
end;
procedure TForm1.Button1Click(Sender: TObject);
var
 R: TRect;
 au, ao: Integer;
 dX, dY, bo, bu: Double;
begin
 // Initialize Mandelbrot
 R.Left := 0;
 R.Right := 200;
 R. := 0;
 R.Bottom := 205;
 ao := 1;
 au := -2;
 bo := 1.5;
 bu := -1.5;
 //direct scaling cause of speed
 dX := (ao - au) / (R.Right - R.Left);
 dY := (bo - bu) / (R.Bottom - R.);
 DrawMandelbrot(Self.Canvas, dX, dY, au, bu, R.Right, R.Bottom);
end;