参考文献/References:
[1] Takagi T.A simple example of the continuous function without derivative [J].Phys Math Soc Japan Ser II,1903(1):176-177.
[2] Kaplan J L,Mallet-Paret J,Yorke J A.The Lyapunov dimension of a nowhere differentiable attracting torus [J].Ergod Th Dynam Sys,1984,4(2):261-281.
[3] Delange H.Sur la fonction sommatoir de la fonction “somme des chiffres” [J].Enseign Math,1975,21(2):31-47.
[4] Buczolich Z.Irregular 1-sets on the graphs of continuous functions [J].Acta Math Hungar,2008,121(4):371-393.
[5] Hata M,Yamaguti M.The Takagi function and its generalization [J].Japan J Appl Math,1984,1(1):183-199.
[6] Trollope J R.An explicit expression for binary digital sums [J].Math Mag,1968,41(1):21-25.
[7] Mirsky L.A theorem on representation of integers in the scale of r [J].Scripta Math,1949,15(1):11-12.
[8] Baba Y.On maxima of Takagi-van der Waerden functions [J].Proc Amer Math Soc,1984,91(3):373-376.
[9] Knuth D E.The art of computer programming,volume 4,fascicle 3:generating all combinations and partitions [M].Upper Saddle River,New Jersey:Addison-Wesley,2005.
[10] Jeffrey C L,Maddock Z.Level sets of the Takagi function:local level sets [J].Monatshefte für Mathematik,2012,166(2):201-238.
[11] 刘爱萍.自相似集迭代函数系统的分离性 [J].江西师范大学学报:自然科学版,2010,34(6):594-596.
[12] Falconer K J.分形几何:数学基础及其应用 [M].曾文曲,刘世耀,戴连贵,等,译.沈阳:东北大学出版社,2001.