为什么曼德布罗特的边界是2?

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我试图理解为什么我们要遍历Mandelbrot点直到| z |. < 4， 为什么是4?有某种法律吗?还是基于统计数据?

I'm trying to understand why we're iterating through Mandelbrot points until |z| < 4. why 4? is there somekind of a law? or is it based on statistical measurements?

感谢，伊加尔

推荐答案

考虑沿y = 0的Mandelbrot集，该集应为z(i) = z(i-1)^2 + c.

Consider the Mandelbrot set with along y=0, which would would be z(i) = z(i-1)^2 + c.

考虑何时c = (x=-2, y=0)

z(0) = 0 z(1) = 0^2 + -2 = -2 z(2) = (-2)^2 + -2 = 4 - 2 = 2 z(3) = 2^2 + -2 = 4 - 2 = 2 z(...) = 2^2 + -2 = 4 - 2 = 2

此示例(x=-2,y=0)是永远不会爆炸的最大量级点.因此，当z^2 > 4时，没有进一步的迭代的意义，因为您已经知道它会爆炸.

This example (x=-2,y=0) is the point with the greatest magnitude that will never blow up. Thus when z^2 > 4, there is no point in further iteration since you already know it will blow up.

所有其他点的数量大于等于2的点都会爆炸.

All other points where the magnitude of the point >= 2 will blow up.