The Mandelbrot set conceals all Julia sets (Workshop ACQUA 2021)

One knows, since the fundamental works of Tan Lei
and Shishikura, that zooming at specific
points of the boundary of the Mandelbrot set may reveal
the Julia set of the corresponding polynomial.
I will explain, by means of elementary methods,
how a similar phenomenon occurs at any point of the boundary of the
Mandelbrot set for the equilibrium measures of these sets.