  We present a simple proof of Tan's theorem on asymptotic similarity between
the Mandelbrot set and Julia sets at Misiurewicz parameters. Then we give a new
perspective on this phenomenon in terms of Zalcman functions, that is, entire
functions generated by applying Zalcman's lemma to complex dynamics. We also
show asymptotic similarity between the tricorn and Julia sets at Misiurewicz
parameters, which is an antiholomorphic counterpart of Tan's theorem.
