de Rham's Function

de Rham's function is the function defined by the functional equations
(Trott 2004, pp. 23-24).
REFERENCES:
Berg, L. and Krüppel, M. "De Rham's Singular Function and Related Functions." Z. Anal. Anwendungen 19, 227-237, 2000.
Berg, L. and Krüppel, M. "De Rham's Singular Function, Two-Scale Difference Equations and Appell Polynomials." Resul. Math. 38, 18-47, 2000.
Kairies, H.-H. "Functional Equations for Peculiar Functions." Aeq. Math. 53, 207-241, 1997.
Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.