5 problems

Let an iterated function system (IFS) generate a self-similar set satisfying the relevant hypotheses, such as the open set condition. Call the IFS non-lattice when its contraction…

Let $n=4$ and let $r$ satisfy $0<r<R_4=1/2$. Then the regular $4$-flake dust is the Cantor dust $\mathcal{F}^{4,r}=C^{1/r}$. The intermediate-ratio Cantor-dust conjecture. For…

Let $C^r$ denote the self-similar fractal family defined in the paper, and let Minkowski measurability mean existence of a finite, positive Minkowski content. The conjecture for…

Let an iterated function system generate a self-similar fractal set satisfying the open set condition. An IFS is non-lattice when its similarity scaling ratios satisfy the correspo…

Principal-complex-dimension conjecture. The presence of a nonreal principal complex dimension is equivalent to $A$ not being Minkowski measurable. Equivalently, $A$ is Minkowski me…