# not “Misiurewicz points” but “Misiurewicz stalks”.

It’s known that at the Misiurewicz points, there’s asymptotic self similarity. But this got me thinking: when we do magnifications of fractals, we’re not really exploring the points that the set is composed of so much as their asymptotic structure, and that asymptote is not zero dimensional information, but a open subset of the plane.

So instead of a Misiurewicz point $M_{n,k}$, we’re really examining the Misiurewicz stalk $\mathcal{F}_{M_{n,k}}$ of the Mandelbrot sheaf $\mathcal{F}$.