How does Mandelbrot's outrage work?

Question

Can someone explain how the outrage described in this article speeds up the rendering of the Mandelbrot set?

I know how to visualize a Mandelbrot set using the traditional method, when many iterations are performed for each pixel, but I do not quite understand what is described in this article.

I calculated the reference orbit as follows:

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; } 

It is right? Then, how to use the reference orbit to calculate all the other pixels?

Answer 1

The Mandelbrot size boundary may be of infinite length, but it is still an infinitesimal part of the entire plane. For most pixels, the document shows how you can calculate a local neighborhood with limited accuracy.

In any case, you work with limited precision ( double ), so this is probably not important to you.