Talk:Fractals/Iterations in the complex plane/Mandelbrot set/mandelbrot

=sqrt=

"x^0.5 is just another way of writing sqrt(x), and yes, it has two solutions. if you perturb sqrt(X) to get sqrt(X+x)-sqrt(X), the perturbation way assumes both square roots should have their solution branches chosen so that the result is "small", and I guess you choose the principal branch for sqrt(X) (the one with Re(sqrt(X) >= 0, and if Re(sqrt(X)) = 0 then the one with Im(sqrt(X) >= 0)). So this perturbation is useful in some mathematical situations where you know which branches you want, but for fractal rendering using perturbation it might not work because sqrt(X) (principal branch) is not continuous." Claude --Adam majewski (discuss • contribs) 06:13, 15 January 2022 (UTC)