Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions

Abstract

The Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is still ongoing. In this paper, we summarize past researchers’ investigations on fractal dimensions of the Weierstrass function graph.

Keywords

• Weierstrass function
• Hausdorff dimension
• box dimension