On Benford’s Law and the Coefficients of the Riemann Mapping Function for the Exterior of the Mandelbrot Set

We investigate Benford's law in relation to fractal geometry. Basic fractals, such as the Cantor set and Sierpinski triangle are obtained limit of iterative sets, unique measures their components follow a geometric distribution, which is Benford most bases. Building on this intuition, we aim study distribution more complicated fractals. examine Laurent coefficients Riemann mapping Taylor its reciprocal function from exterior Mandelbrot complement unit disk. These 2-adic rational numbers, through statistical testing, demonstrate that numerators denominators good fit for law. offer additional conjectures observations about these coefficients. In particular, highlight certain arithmetic subsequences related coefficients' denominators, provide an estimate slope, describe efficient methods compute them.