Radix expansions and connectedness of planar self-affine fractals.

Let A be an expanding matrix with characteristic polynomial f (x) = x 2 + p x + 3 and D = { 0 , v , ℓ v + k A v } be a digit set where ℓ , k ∈ Z , v ∈ R 2 so that { v , A v } is linearly independent. It is well known that there exists a unique self-affine fractal T satisfying A T = T + D . In this paper, we give a complete characterization for the connectedness of T by using radix expansion. [ABSTRACT FROM AUTHOR]