An analogue of Cobham’s theorem for fractals
An analogue of Cobham’s theorem for fractals
We introduce the notion of $k$-self-similarity for compact subsets of $\mathbb {R}^n$ and show that it is a natural analogue of the notion of $k$-automatic subsets of integers. We show that various well-known fractals such as the triadic Cantor set, the SierpiÅski carpet or the Menger sponge turn out to …