Portraits of orthogonal matrices as a base for discrete textile ornament patterns

Abstract

Computers can be used in modern textile industry for generating “portraits” of orthogonal matrices as unique rapports for creating ornament patterns. We propose to use computationally difficult unique matrices with two features, namely, orthogonality and symmetry. Such matrices are unique both mathematically and graphically, as they can be symmetric, circulant, and multi-circulant at the same time. We provide examples of symmetric Hadamard matrices with features of matrix portrait fractality.