Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof

Following the ideas of A.~Douady, we give an alternative proof of the authors’ result: for any boundary point $c_0$ of the Mandelbrot set $M$, we can find small quasiconformal copies of $M$ in $M$ that are encaged in nested quasiconformal copies of the totally disconnected Julia set of a parameter arbitrarily close to $c_0$.