The escape-time atlas conjecture for twisted tent maps

Let $c$ be a parameter in the parameter plane, let $K(c)$ be the associated filled-in set, and let the polygonal locus denote the parameter-space locus discussed in the source. An escape-time picture is the parameter-plane coloring obtained by recording escape behavior from a chosen test point. Escape-time atlas conjecture. Drawing an escape-time picture of the parameter plane using a test point very close to $0$ produces an atlas of $K$'s with empty interior all around the outside of the polygonal locus. The claim is explicitly motivated by experimental inspection of a parameter-plane figure; no resolution is given in the supplied text.