Bragg Diffraction of One Dimensional Substitution Tilings

Abstract

This project presents tools for modeling and visualizing one dimensional substitution tilings as well as calculating and displaying their Bragg Diffraction patterns. The application is rather robust in that it allows the user to define a particular substitution, then displays visuals based on the defined substitution, erroring out if the substitution is invalid. The application also includes a set of some of the best-known one-dimensional substitutions, from which you can select from. For a given substitution the application can generate a segment diagram, calculate the PF Eigenvector, determine if the substitution is “Pisot”, generate a symbolic text representation of the substitution, plot a diffraction intensity graph, and generate a project of the Bragg diffraction pattern.

Department: Mathematics and Statistics

Faculty Mentor: Dr. Nicolae Strungaru