Mandelbrot Fractal不工作

Question

我试着做了这个Mandelbrot分形发生器，但是当我运行它时，我得到了一个像圆圈一样的输出。不知道为什么会发生这种事。我认为我的颜色可能有问题，但即使是这样，形状也不正确。

public static Bitmap Generate(
        int width,
        int height,
        double realMin,
        double realMax,
        double imaginaryMin,
        double imaginaryMax,
        int maxIterations,
        int bound)
    {
        var bitmap = new FastBitmap(width, height);
        var planeWidth = Math.Abs(realMin) + Math.Abs(realMax); // Total width of the plane.
        var planeHeight = Math.Abs(imaginaryMin) + Math.Abs(imaginaryMax); // Total height of the plane.
        var realStep = planeWidth / width; // Amount to step by on the real axis per pixel.
        var imaginaryStep = planeHeight / height; // Amount to step by on the imaginary axis per pixel.
        var realScaling = width / planeWidth;
        var imaginaryScaling = height / planeHeight;
        var boundSquared = bound ^ 2;
        for (var real = realMin; real <= realMax; real += realStep) // Loop through the real axis.
        {
            for (var imaginary = imaginaryMin; imaginary <= imaginaryMax; imaginary += imaginaryStep) // Loop through the imaginary axis.
            {
                var z = Complex.Zero;
                var c = new Complex(real, imaginary);
                var iterations = 0;
                for (; iterations < maxIterations; iterations++)
                {
                    z = z * z + c;
                    if (z.Real * z.Real + z.Imaginary * z.Imaginary > boundSquared)
                    {
                        break;
                    }
                }
                if (iterations == maxIterations)
                {
                    bitmap.SetPixel(
                        (int)((real + Math.Abs(realMin)) * realScaling),
                        (int)((imaginary + Math.Abs(imaginaryMin)) * imaginaryScaling),
                        Color.Black);
                }
                else
                {
                    var nsmooth = iterations + 1 - Math.Log(Math.Log(Complex.Abs(z))) / Math.Log(2);
                    var color = MathHelper.HsvToRgb(0.95f + 10 * nsmooth, 0.6, 1.0);
                    bitmap.SetPixel(
                        (int)((real + Math.Abs(realMin)) * realScaling),
                        (int)((imaginary + Math.Abs(imaginaryMin)) * imaginaryScaling),
                        color);
                }
            }
        }
        return bitmap.Bitmap;
    }

Answer 1

这里有一个错误：

var boundSquared = bound ^ 2;

这应该是：

var boundSquared = bound * bound;

^运算符的意思是xor。