Differentiability of a two-parameter family of self-affine functions

This paper highlights an unexpected connection between expansions of real numbers to noninteger bases (so-called β-expansions) and the infinite derivatives of a class of self-affine functions. Precisely, we extend Okamoto's function (itself a generalization of the well-known functions of Perkins and Katsuura) to a two-parameter family {FN,a:N∈N,1/(N+1)