C# MandelBrot分形图绘制

一。代码

注：这里为了制造多个渲染效果使用委托类来当作函数指针使用。 

        private  static Random rn = new Random();     
        private  delegate UInt32 _dg_GetUint32Color(int i);

        private const int mb_iteration = 24; //迭代次数限制

        private static _dg_GetUint32Color[] _mbGetColors = new _dg_GetUint32Color[3];
        //颜色迭代 委托
        private static _dg_GetUint32Color mbGetColor = _mbGetColorA;
        //三个颜色函数，直接影响渲染效果
        private static UInt32 _mbGetColorA(int it)
        {
            UInt32 n = (UInt32)it * 8;
            UInt32 r, g, b;
            UInt32 old = n;

            n = n % 255;

            if (old < 255)
            {
                g = 255 - n;
                b = n;
                r = 0;
            }
            else
                if (old < 255 * 2)
                {
                    g = 0;
                    b = 255 - n;
                    r = n;
                }
                else
                {

                    g = n;
                    b = 0;
                    r = 255 - n;

                }

            return  0xff000000+(r<<16)+(g<<8)+(b) ;
        }
        private static UInt32 _mbGetColorB(int it)
        {
            UInt32 n = (UInt32)it * 8;
            UInt32 r, g, b;
            UInt32 old = n;

            n = n % 255;

            if (old < 255)
            {
                b = 255 - n;
                r = n;
                g = 0;
            }
            else
                if (old < 255 * 2)
                {
                    b = 0;
                    r = 255 - n;
                    g = n;
                }
                else
                {

                    b = n;
                    r = 0;
                    g = 255 - n;

                }

            return 0xff000000 + (r << 16) + (g << 8) + (b);
        }
        private static UInt32 _mbGetColorC(int it)
        {
            UInt32 n = (UInt32)it * 8;
            UInt32 r, g, b;
            UInt32 old = n;

            n = n % 255;

            if (old < 255)
            {
                r = 255 - n;
                b = n;
                g = 0;
            }
            else
                if (old < 255 * 2)
                {
                    r = 0;
                    b = 255 - n;
                    g = n;
                }
                else
                {

                    r = n;
                    b = 0;
                    g = 255 - n;

                }

            return 0xff000000 + (r << 16) + (g << 8) + (b);
        }

 这是MandelBrot核心函数，如果固定公式的cc，再修改一下就是Julia分形。

        /// 

        /// 迭代
        /// 
        /// 复数
        /// 阶数
        /// 32bit颜色
        private static UInt32 _mandelbrot(Complex cc, byte n)
        {
            Complex z = new Complex(0, 0);

            for (int i = 0; i < mb_iteration; i++)
            {
              
                // if (z.square > 4) return _mbGetColorB(i); 

                if (z.square > 4) return mbGetColor((int)(z.real) * (10 - n)); 

                z = Complex.pow(z, n) + cc;
            }

            return 0xFF000000;//背景色
        }

如果直接操作gs进行一点一点地绘图，也行，但是慢，所以这里直接使用指针（虽然C#不推荐使用指针）。 其实运行程序的时间基本耗在上面的迭代函数，与绘图方式关系不大。（单纯的绘图，使用指针比使用gs画点快几十倍!）

        /// 

        /// 分形Mandelbrot
        /// 
        /// 画面
        /// 面积
        /// 阶数
       unsafe public static void DrawMandelbrot(Graphics gs, Size s, byte n)
        {
            _mbGetColors[0] = _mbGetColorA;
            _mbGetColors[1] = _mbGetColorB;
            _mbGetColors[2] = _mbGetColorC;

            mbGetColor = _mbGetColors[rn.Next(3)];

            double par = 1;//系数
            double offsetx=0, offsety=0;//偏移

            Bitmap srcbmp = new Bitmap(s.Width ,s.Height);
            BitmapData bmpData = srcbmp.LockBits(new Rectangle(0, 0, srcbmp.Width, srcbmp.Height), ImageLockMode.ReadWrite, PixelFormat.Format32bppArgb);
            UInt32 stride = (UInt32)bmpData.Stride;
            byte* srcbuf = (byte*)bmpData.Scan0.ToPointer();

            double xx=0, yy=0;
            Complex cc = new Complex(0,0);
            for (UInt32 j = 0; j < s.Height; j++)
            {
                yy = ((double)j / s.Width) * 4 * (par) - 2 * (par);
                for (UInt32 i = 0; i < s.Width; i++)
                {
                    
                    xx = ((double)i / s.Height) * 4 * (par) - 2 * (par);
                    cc = new Complex(xx + offsetx, yy + offsety);
                   
                    UInt32* ptr = (UInt32*)(srcbuf + i * 4 + j * stride);
                    *ptr = _mandelbrot(cc, n);
                }
            }
            srcbmp.UnlockBits(bmpData);
            gs.DrawImage(srcbmp,0,0);
            srcbmp.Dispose();
        }

 

二。效果图

 MandelBrot分形：二阶图像，渲染的颜色单调

 调整渲染参数：

多阶图像

再试试Julia分形