着色曼德尔布罗集
我想到了这样的事情：
float MinRe = -2.0f; // real
float MaxRe = 1.0f;
float MinIm = -1.0f; // imaginary
float MaxIm = MinIm + (MaxRe - MinRe) * WindowData.Height / WindowData.Width;
float Re_factor = (MaxRe - MinRe) / (WindowData.Width - 1);
float Im_factor = (MaxIm - MinIm) / (WindowData.Height - 1);
int MaxIterations = 50;
int iter=0;
for (int y = 0; y < WindowData.Height; ++y)
{
double c_im = MaxIm - y * Im_factor; // complex imaginary
for (int x = 0; x < WindowData.Width; ++x)
{
double c_re = MinRe + x * Re_factor; // complex real
// calculate mandelbrot set
double Z_re = c_re, Z_im = c_im; // Set Z = c
bool isInside = true;
for (iter=0; iter < MaxIterations; ++iter)
{
double Z_re2 = Z_re * Z_re, Z_im2 = Z_im * Z_im;
if (Z_re2 + Z_im2 > 4)
{
isInside = false;
break;
}
Z_im = 2 * Z_re * Z_im + c_im;
Z_re = Z_re2 - Z_im2 + c_re;
}
if(isInside)
{
GL.Color3(0, 0, 0);
GL.Vertex2(x, y);
}
}
}
我尝试了几种方法，但大多数时候都以周围的单色或整个屏幕的相同颜色结束。
如何正确设置颜色？
I have came up to something like this:
float MinRe = -2.0f; // real
float MaxRe = 1.0f;
float MinIm = -1.0f; // imaginary
float MaxIm = MinIm + (MaxRe - MinRe) * WindowData.Height / WindowData.Width;
float Re_factor = (MaxRe - MinRe) / (WindowData.Width - 1);
float Im_factor = (MaxIm - MinIm) / (WindowData.Height - 1);
int MaxIterations = 50;
int iter=0;
for (int y = 0; y < WindowData.Height; ++y)
{
double c_im = MaxIm - y * Im_factor; // complex imaginary
for (int x = 0; x < WindowData.Width; ++x)
{
double c_re = MinRe + x * Re_factor; // complex real
// calculate mandelbrot set
double Z_re = c_re, Z_im = c_im; // Set Z = c
bool isInside = true;
for (iter=0; iter < MaxIterations; ++iter)
{
double Z_re2 = Z_re * Z_re, Z_im2 = Z_im * Z_im;
if (Z_re2 + Z_im2 > 4)
{
isInside = false;
break;
}
Z_im = 2 * Z_re * Z_im + c_im;
Z_re = Z_re2 - Z_im2 + c_re;
}
if(isInside)
{
GL.Color3(0, 0, 0);
GL.Vertex2(x, y);
}
}
}
I have tried in few ways, but most of the times ended with single color around set, or whole screen with the same color.
How to set up colors properly?
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评论（4）
当我尝试这个时，我只是将外部颜色设置为 RGB (value, value, 1)，其中 value 是（用你的话说）
(iter / MaxIterations)的第四个根。结果是从白色到蓝色的渐变非常漂亮。虽然不如达菲莫那么明亮，但“条纹”效果较少。When I tried this, I just set the outside colour to RGB (value, value, 1) where value is (in your parlance) the fourth root of
(iter / MaxIterations). That comes out as a quite nice fade from white to blue. Not so bright as duffymo's, though, but with less of a 'stripy' effect.我是这样做的：查看 Source Forge 存储库中的源代码。
http://craicpropagation.blogspot.com/2011/03/mandelbrot-set.html
Here's how I did it: check out the Source Forge repository for source code.
http://craicpropagation.blogspot.com/2011/03/mandelbrot-set.html
我根据经验发现，如果你使用类似的东西： color(R,G,B) 其中 R,G,B 的值从 0 到 255。
那么这个函数会给出一个非常漂亮的结果。
f(x,f,p) = 255*(cos(sqrt(x)*f + p))^2其中x表示当前迭代，f频率和p相位。然后对相位差为 120 的每个颜色参数应用该函数：
color(f(iter,1,0),f(iter,1,120),f(iter,1,240)I found empirically that if you use something like that: color(R,G,B) where R,G,B takes values from 0 to 255.
Then this function gives a really good looking result.
f(x,f,p) = 255*(cos(sqrt(x)*f + p))^2wherexdenotes the current iteration,fthe frequency andpthe phase.And then apply the function for each color argument with a phase difference of 120:
color(f(iter,1,0),f(iter,1,120),f(iter,1,240)尝试显示您的计算结果。检查着色函数需要什么输入
另请参阅
http://en.wikibooks.org/ wiki/分形/Iterations_in_the_complex_plane/Mandelbrot_set
HTH
Adam
try to display result of your computation. Check what input is required by your coloring function
See also
http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set
HTH
Adam