On a class of fractals: the constructive structure

In the present paper, we consider the following generalization of Besicovitch functions. Let {λn} satisfy Hadamard condition, writef(t)=∑∞n=1ancosλnt. We are interested in the intrinsic relationship among the coefficients {an}, the modulus of continuity of f and the upper Box dimension of graph of f. Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware.