On the transfer matrices of fractals Original Research Article

An algebra of matrices of order 2n was introduced by Mandelbrot et al. Some of these matrices are associated with iterative constructions of fractal objects and for this reason are called TMFs (transfer matrices of fractals). It has been proved that the eigenvalues of a TMF are nonnegative integers. In this article TMFs are shown to be diagonalizable, and further properties of these matrices, as well as some of their generalizations, are investigated.