Nonperiodic tilings related to Stern's diatomic series and based on tiles decorated with elements of $\mathbb{F}_p$

Abstract

This paper presents the construction and various properties of substitution tilings related to Stern's diatomic series and based on tiles decorated with elements of $\mathbb{F}_p$ for some odd prime number $p$. These substitution tilings are additive in a sense that will be clarified later and lead to new nonperiodic tilings in one and two dimensions.