How does Mandelbrot perturbation work?

问题

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

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.

I compute the reference orbit like this:

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;
}

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

回答1:

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.

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

来源：https://stackoverflow.com/questions/25640013/how-does-mandelbrot-perturbation-work