A dimension formula of a class of fractal surfaces

  • Authors:

  • Huikun Jiang

  • Affiliations:

  • State Key Lab. for Novel Software Technology, Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China

  • Venue:
  • Analysis, combinatorics and computing
  • Year:
  • 2002

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Abstract

In this paper, we consider the fractal dimension of a class of surfaces generated by a boundary value problem of a fourth-order difference equation. A natural dimension formula is obtained. The main result says that: If the graph of the boundary function in the boundary value problem is of box dimension γ, then the solution surface is of box dimension 1 + γ.