Автор: http://www.swissdelphicenter.ch

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.Top := 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.Top);
  DrawMandelbrot(Self.Canvas, dX, dY, au, bu, R.Right, R.Bottom);
end;