Chapter 8 – Fractal Surfaces

Publisher Summary This chapter discusses IRm -valued multivariate continuous fractal functions and some of their properties. It presents tensor product fractal surfaces and the way tensor product can be used to obtain fractal-like surfaces from univariate IR-valued continuous fractal functions. The chapter also presents nontensor product fractal surfaces defined on certain polyhedra in IRn. It presents the construction of nontensor product fractal surfaces in a general setting. This construction is based on recurrent iterated function systems and emphasizes the interpolatory nature of fractal surfaces in IRn + m. The chapter also discusses some properties of fractal surfaces. Among those are oscillation, regularity and differentiability, Holder continuity, and the box dimension. It presents the way moments of IR-valued multivariate fractal functions can be recursively calculated.