Division Point Measures from Primitive Substitutions

Abstract

In this note we extend results of Olli concerning limits of point measures arising from substitutions. We consider a general primitive substitution on a finite polygon set in ${\mathbb{R}}^2$ and show that limits of certain atomic measures each converge to Lebesgue measure.

arXiv comment13 Pages, 4 Figures. Third version adds references and fixes typos and other minor errors. To appear in Expositiones Mathematicae