c++ - 如何给 Mandelbrot 着色？

Question

在学习了这个为您提供所有代码 (http://warp.povusers.org/Mandelbrot/) 的非常简单的教程之后，我没有任何运气可以弄清楚如何像图片中那样为轮廓着色。

If in our example we map n to a color so that from 0 to MaxIterations/2-1 the color goes from black to red and from MaxIterations/2 to MaxIterations-1 the color goes from red to white, we get the following image:

void compute_mandelbrot(double left, double right, double top, double bottom, double start, double end) //improved mandelbort following a tutorial
{
    double ImageHeight = 960;
    double ImageWidth = 960;

    //double MinRe = -2.5;
    //double MaxRe = 1.25;
    //double MinIm = -1.2;
    double MinRe = left;
    double MaxRe = right;
    double MinIm = top;
    double MaxIm = MinIm + (MaxRe - MinRe)*ImageHeight / ImageWidth;
    double Re_factor = (MaxRe - MinRe) / (ImageWidth - 1);
    double Im_factor = (MaxIm - MinIm) / (ImageHeight - 1);
    //unsigned MAX_ITERATIONS = 100;

    /*int r = 0x00, g = 0x00, b = 0x00;*/


    for (unsigned y = 0; y<ImageHeight; ++y)
    {
        double c_im = MaxIm - y*Im_factor;
        for (unsigned x = 0; x<ImageWidth; ++x)
        {
            //vertex.color = sf::Color(255, 255, 255, 255);
            //r = g = b = 0;

            double c_re = MinRe + x*Re_factor;

            double Z_re = c_re, Z_im = c_im;
            bool isInside = true;
            for (unsigned n = 0; n<MAX_ITERATIONS; ++n)
            {
                //vertex.color = sf::Color(0, 0, 0, 255); //figure is black
                //vertex.color = sf::Color(255, 255, 255, 255); //figure is white
                r = g = b = 0;

                double Z_re2 = Z_re*Z_re, Z_im2 = Z_im*Z_im;
                if (Z_re2 + Z_im2 > 4)
                {

                    isInside = false;

                    auto half = MAX_ITERATIONS / 2.0;

                    if (n < half) {
                        r = n / half * 255;
                    }
                    else {
                        r = 255;
                        g = b = (n - half) / half * 255;
                    }

                    vertex.color = sf::Color(r, g, b, 255);

                    break;
                }

                Z_im = 2 * Z_re*Z_im + c_im;
                Z_re = Z_re2 - Z_im2 + c_re;


            }

            if (isInside)
            {
                //vertex.color = sf::Color(r, g, b, 255); //line pattern

                mutex.lock();
                vertex.position = sf::Vector2f(x, y);
                varray.append(vertex);
                mutex.unlock();
            } 
        }
    }



}

我不认为我明白我打算在那里做什么，我尝试了一些东西，包括代码中的内容，但没有成功。

Answer 1

在 isInside = false; 行，您有一个 n 值，该点在该位置处脱离了集合。使用此 n 值根据您的颜色偏好设置点的 r、g、b 值。如果该点没有逃脱，它将是黑色的(或者任何你初始化 r、g 和 b 的东西)。

map n to a color so that from 0 to MaxIterations/2-1 the color goes from black to red and from MaxIterations/2 to MaxIterations-1 the color goes from red to white

这是简单的 RGB 数学，例如

auto half = MaxIterations/2.0;

if( n < half ) {
  r = n / half;
}else {
  r = 1.0;
  g = b = (n - half) / half;
}

它给出 0-1 范围内的 rgb，如果您使用整数作为颜色则乘以 255