The tilings encyclopedia shows a wealth of examples of nonperiodic substitution tilings. Click on "substitutions" to browse the list or to search for a topic (e.g. "Penrose" or "fractal" or ...). We welcome all feedback. If you cite this page as a reference in a scientific paper, please cite as: D. Frettlöh, E. Harriss, F. Gähler: Tilings encyclopedia, https://tilings.math.uni-bielefeld.de/
Socolar found the basis for this tiling already in 1987, but recently added a substitution tiling. An interesting feature is that there exists a context-independent Ammann bar decoration of the tiles, similar to the one in the original Socolar 12-fold but with different relative phases, and hence a fairly simple set of matching rules.
Self Similar Substitution
10-fold cyclotomic aperiodic tiling with dense tile orientations (CAST DTO).
8-fold cyclotomic aperiodic tiling with dense tile orientations (CAST DTO).