![]() The dynamical system $z\mapsto P(z)$ is stable under a perturbation of $P$ if and only if $c\in \partial M$, where $\partial $ is a notation for the topological boundary.The Julia set of $P$ is connected if and only if $c\in M$.If you do not know any of the italicized words, go and look on the Internet. The Mandelbrot set, denoted M, is the set of complex numbers $c$ such that the critical point $z=0$ of the polynomial $P(z)=z^2+c$ has an orbit that is not attracted to infinity. Here I give a very quick definition/reminder: 3.5.3 Variation: using the distance estimator to color the outsideĬertainly, Wikipedia's page about this set in any language should be a good introduction.3.5.2 Variation: (partial) antialias effect without oversampling.3.5 Boundary detection methods via distance estimators.3.4.1 Math digression: hyperbolic components.3.3.1 Deep zooms and log-potential scale.
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