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 .




using System;
using System.Drawing;
using System.Drawing.Imaging;
using System.Threading;
using System.Windows.Forms;
 
/// <summary>
/// Generates bitmap of Mandelbrot Set and display it on the form.
/// </summary>
public class MandelbrotSetForm : Form
{
    const double MaxValueExtent = 2.0;
    Thread thread;
 
    static double CalcMandelbrotSetColor(ComplexNumber c)
    {
        // from http://en.wikipedia.org/w/index.php?title=Mandelbrot_set
        const int MaxIterations = 1000;
        const double MaxNorm = MaxValueExtent * MaxValueExtent;
 
        int iteration = 0;
        ComplexNumber z = new ComplexNumber();
        do
        {
            z = z * z + c;
            iteration++;
        } while (z.Norm() < MaxNorm && iteration < MaxIterations);
        if (iteration < MaxIterations)
            return (double)iteration / MaxIterations;
        else
            return 0; // black
    }
 
    static void GenerateBitmap(Bitmap bitmap)
    {
        double scale = 2 * MaxValueExtent / Math.Min(bitmap.Width, bitmap.Height);
        for (int i = 0; i < bitmap.Height; i++)
        {
            double y = (bitmap.Height / 2 - i) * scale;
            for (int j = 0; j < bitmap.Width; j++)
            {
                double x = (j - bitmap.Width / 2) * scale;
                double color = CalcMandelbrotSetColor(new ComplexNumber(x, y));
                bitmap.SetPixel(j, i, GetColor(color));
            }
        }
    }
 
    static Color GetColor(double value)
    {
        const double MaxColor = 256;
        const double ContrastValue = 0.2;
        return Color.FromArgb(0, 0,
            (int)(MaxColor * Math.Pow(value, ContrastValue)));
    }
 
    public MandelbrotSetForm()
    {
        // form creation
        this.Text = "Mandelbrot Set Drawing";
        this.BackColor = System.Drawing.Color.Black;
        this.BackgroundImageLayout = System.Windows.Forms.ImageLayout.Stretch;
        this.MaximizeBox = false;
        this.StartPosition = FormStartPosition.CenterScreen;
        this.FormBorderStyle = FormBorderStyle.FixedDialog;
        this.ClientSize = new Size(640, 640);
        this.Load += new System.EventHandler(this.MainForm_Load);
    }
 
    void MainForm_Load(object sender, EventArgs e)
    {
        thread = new Thread(thread_Proc);
        thread.IsBackground = true;
        thread.Start(this.ClientSize);
    }
 
    void thread_Proc(object args)
    {
        // start from small image to provide instant display for user
        Size size = (Size)args;
        int width = 16;
        while (width * 2 < size.Width)
        {
            int height = width * size.Height / size.Width;
            Bitmap bitmap = new Bitmap(width, height, PixelFormat.Format24bppRgb);
            GenerateBitmap(bitmap);
            this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), bitmap);
            width *= 2;
            Thread.Sleep(200);
        }
        // then generate final image
        Bitmap finalBitmap = new Bitmap(size.Width, size.Height, PixelFormat.Format24bppRgb);
        GenerateBitmap(finalBitmap);
        this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), finalBitmap);
    }
 
    void SetNewBitmap(Bitmap image)
    {
        if (this.BackgroundImage != null)
            this.BackgroundImage.Dispose();
        this.BackgroundImage = image;
    }
 
    delegate void SetNewBitmapDelegate(Bitmap image);
 
    static void Main()
    {
        Application.Run(new MandelbrotSetForm());
    }
}
 
struct ComplexNumber
{
    public double Re;
    public double Im;
 
    public ComplexNumber(double re, double im)
    {
        this.Re = re;
        this.Im = im;
    }
 
    public static ComplexNumber operator +(ComplexNumber x, ComplexNumber y)
    {
        return new ComplexNumber(x.Re + y.Re, x.Im + y.Im);
    }
 
    public static ComplexNumber operator *(ComplexNumber x, ComplexNumber y)
    {
        return new ComplexNumber(x.Re * y.Re - x.Im * y.Im,
            x.Re * y.Im + x.Im * y.Re);
    }
 
    public double Norm()
    {
        return Re * Re + Im * Im;
    }
}