Shrinking-hole density conjecture for the boundary of the Mandelbrot set

Let ${\mathcal M}$ be the parameter set under consideration, and let $\partial {\mathcal M}$ denote its boundary. A hole is a connected component of the complement of ${\mathcal M}$, and its diameter is measured in the ambient parameter plane. Shrinking-hole density conjecture. Every point in $\partial {\mathcal M}$ not on the real axis is a limit of a sequence of holes with diameters going to zero. The conjecture describes how the exotic holes accumulate on the non-real part of the boundary. The supplied text gives no proof or disproof.