Non-affine fractal hypersurfaces: construction and dimensions

Abstract

This article presents the construction of a non-affine hypersurface on an $n$-simplex in ${\mathbb{R}}^n$. Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain conditions. Furthermore, the upper bound of the Hausdorff dimension of the invariant probability measure supported on the graph of such fractal function is estimated.