The Box Dimensions Of Graphs Of The Weierstrass-type Functions

Fractal geometry is a description of the structure of the natural patterns ofthe new geometry. It is created by American mathematician B.B.Mandelbrot[9]the late 1970s. It is very irregular to the geometric figure for the research, usingvarious mathematical tools to capture such irregular. Because of this irregularin a variety of fields ?ourished, it increasingly associated physical, chemical,biological, calculators and so on. This was exactly that in recent years, therapid development of fractal geometry as a newly-developed discipline.The Weierstrass function is the no place differentiable and continuous func-tion. Because the infinite summation caused the function to have the fine struc-ture and everywhere does not have the tangent. It cannot like smooth curve thatis possible to use the classics the calculus to study. Therefore, We use the frac-tal geometry method to study the Weierstrass-type functions frequently. In thispaper, we mainly discuss the Box dimensions of the Weierstrass-type functions.Firstly, the Box dimension of the graph of the Weierstrass functionis studied, and some su?cient conditions of Weierstrass functions with graph Boxdimension 2 are given. We structure a class of functions satisfied the suffcientconditions. And these conditions are easier than T.F.Xie and S.P.Zhou's[16].Secondly, we discuss the more common, no place di?erentiable and continuous...