Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

DIMENSIONS OF INTERSECTIONS OF THE SIERPINSKI CARPET WITH LINES OF RATIONAL SLOPES

Qing-Hui Liua1, Li-Feng Xia2 and Yan-Fen Zhaoa3

a1 Department of Computer Science and Engineering, Beijing Institute of Technology, 100080, Beijing, China (qhliu@bit.edu.cn)

a2 Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, China (xilifengningbo@yahoo.com)

a3 Department of Mathematics, Wuhan University, Wuhan, 430062, Hubei, China (wangzhaoyanfen@hotmail.com)

Abstract

This paper computes the Box and Hausdorff dimensions of the intersections of the Sierpinski carpet with planar lines of rational slopes.

(Received March 30 2005)

Keywords

  • Primary 28A80;
  • fractal;
  • Sierpinski carpet;
  • dimension;
  • ergodic theory