LinqPad Compatible Fractal Drawing

NewtonFractal.cs

/* Idea and clojure from http://nakkaya.com/2010/04/20/fractals-in-clojure-newton-fractal */
Func<Complex, Complex> f1 = c => (c * c * c) - Complex.One;
Func<Complex, Complex> f2 = c => ((c * c * c) - (c * 2)) + 2; 
Func<Complex, Complex> f3 = c => new Complex(Math.Sin(c.Real) * Math.Cosh(c.Imaginary),
                                             Math.Cos(c.Real) * Math.Sinh(c.Imaginary));
Func<Complex, Complex> f4 = c => (c * c * c * c) - Complex.One; 

double step = 0.000006;
double delta = 0.003;
Tuple<int,int> formDimensions = new Tuple<int,int>(800, 600);
Tuple<double,double,double,double> complexPane = new Tuple<double,double,double,double>(-1.3d, 1.4d, -1.0d, 1.0d);

Func<Complex, Complex> activeFunction = null;

[STAThread]
void Main()
{
    activeFunction = f2;

    Form form = new Form();
    form.Width = formDimensions.Item1;
    form.Height = formDimensions.Item2;
    form.ResizeEnd += (sender, evt) => formDimensions = new Tuple<int,int>(((Control)sender).Size.Width, ((Control)sender).Size.Height);
    form.Paint += (sender, evt) => Draw(activeFunction, evt.Graphics);
    form.Show();

    var g = form.CreateGraphics();
    Draw(activeFunction, g);
 
    form.Show();
    form.Activate();
    Application.Run(form);
}

Bitmap Newton(Func<Complex,Complex> f, double step, double delta, Tuple<int,int> dimensions, Tuple<double,double,double,double> complexPane)
{
    var width = dimensions.Item1;
    var height = dimensions.Item2;
    var xa = complexPane.Item1;
    var xb = complexPane.Item2;
    var ya = complexPane.Item3;
    var yb = complexPane.Item4;
    var sw =  new Stopwatch();
    sw.Start();
    var results = new int[width, height];
    
    var b = new Bitmap(width, height);
    Parallel.For(0, width, x => {
        Parallel.For(0, height, y => {
            var zx = (((xb - xa) * x) / (width - 1)) + xa;
            var zy = (((yb - ya) * y) / (height - 1)) + ya;
            var c = Converge(f, new Complex(zx, zy), step, delta);
            results[x,y] = c;
        });
    });
    
    Console.WriteLine ("Newton took: " + sw.ElapsedMilliseconds + "ms.");
    sw.Restart();
    for (int y = 0; y < height; y++)
    {
        for (int x = 0; x < width; x++)
        {
            var c = results[x,y];
            var color = Color.FromArgb(255, (c % 4) * 64, (c % 8) * 32, (c % 16) * 16);
            b.SetPixel(x,y, color);
        }
    }
    Console.WriteLine ("Bitmap creation took: " + sw.ElapsedMilliseconds + "ms.");
    return b;
}

int Converge(Func<Complex,Complex> f, Complex c, double step, double delta)
{
    Func<Complex, Complex> dz = p => (f(p + new Complex(step, step)) - f(p)) / new Complex(step, step);
    Func<Complex, Complex> iter = p => Complex.Subtract(p, Complex.Divide(f(p), dz(p))); 

    var lz = c;
    var z = iter(c);
    for (int i = 0; i <= 32; i++)
    {
        if(i > 31 || Complex.Abs(Complex.Subtract(z, lz)) < delta)
            return i;
            
        lz = z;
        z = iter(z);
    }
    return 32;
}

void Draw(Func<Complex,Complex> f, Graphics graphics) 
{   
    var sw = new Stopwatch();
    sw.Start();

    var fractalBitmap = Newton(f, step, delta, formDimensions, complexPane);
    graphics.DrawImage(fractalBitmap, 0, 0);
    
    Console.WriteLine("Finished Drawing after " + sw.ElapsedMilliseconds + "ms.");
}