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

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.