  An intermittent nonlinear map generating subdiffusion is investigated.
Computer simulations show that the generalized diffusion coefficient of this
map has a fractal, discontinuous dependence on control parameters. An amended
continuous time random walk theory well approximates the coarse behavior of
this quantity in terms of a continuous function. This theory also reproduces a
full suppression of the strength of diffusion, which occurs at the dynamical
phase transition from one type of diffusive behavior to another. Similarly, the
probability density function of this map exhibits a nontrivial fine structure
while its coarse functional form is governed by a time fractional diffusion
equation. A more detailed understanding of the irregular structure of the
generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo
formula establishing a relation to de Rham-type fractal functions.
