Mandelbrot扰动如何工作? [英] How does Mandelbrot perturbation work?

问题描述

有人可以解释一下本文中描述的扰动如何加速Mandelbrot集的渲染吗?

Could someone please explain how perturbation described in this paper accelerates rendering the Mandelbrot set?

我知道如何使用传统方法渲染Mandelbrot集，其中对每个像素执行多次迭代，但是我不太理解该论文中所描述的内容.

I know how to render the Mandelbrot set using the traditional method where many iterations are performed for each pixel, but I don't quite understand what is being described in that paper.

我这样计算参考轨道:

std::complex<double> Xo(some_x, some_y);
std::complex<double> Xn(0,0);

for (int n = 0; n < maxIterations; ++n) {
  orbit.push_back(Xn);
  Xn = Xn * Xn + Xo;
}

那是正确的吗?那么如何使用参考轨道来计算所有其他像素?

Is that correct? Then how do I use the reference orbit to compute all the other pixels?

推荐答案

Mandelbrot大小的边界可能有无限长，但是仍然是整个平面的无限小部分.对于大多数像素，本文说明了如何以有限的精度计算局部邻域.

The border of the Mandelbrot size may have infinite length, but it's still an infinitely small part of the whole plane. For most pixels, the paper shows how you can calculate the local neighbourhood in limited precision.

无论如何，您的精度都受到限制(double)，所以对您来说可能并不重要.

You're working with a limited precision anyway (double) so it probably doesn't matter for you.

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