We study the distribution of harmonic measure on connected Julia sets of unicritical polynomials. Harmonic measure on a full compact set in ℂ is always concentrated on a set which is porous for a positive density of scales. We prove that there is a topologically generic set $\mathcal{A}$ in the boundary of the Mandelbrot set such that for every $c\in \mathcal{A}$ ,$β$>0, and$λ$∈(0,1), the corresponding Julia set is a full compact set with harmonic measure concentrated on a set which is not$β$-porous in scale$λ$^{$n$}for$n$from a set with positive density amongst natural numbers.