Dimensions of difference-algebraic groups

Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point $x$ in such a fractal $F$ arising from an IFS $S$ is naturally ...

In this paper we use Conway's surreal numbers to define a refinement of the box-counting dimension of a subset of a metric space. The surreal dimension of such a subset is well-defined in many cases in which the box-counting dimension is not. Surreal ...