A Class of Two-Dimensional Model Sets from One-Dimensional Substitutions

Explore a mathematical lecture on two-dimensional model sets derived from one-dimensional substitutions. Delve into the Fibonacci symbolic substitution, cut-and-project schemes, and renormalization for windows. Examine Fibinoid direct product substitutions, inflate-and-subdivide rules, and 3D stepped surfaces. Investigate Fibonacci direct product substitutions, measure-theoretic situations, and 28 polygonal windows. Learn about Rauzy fractal islands, castles, and window comparisons. Discover Park-Robinson's Chacon Z action and non-Pisot direct product variations. Analyze finite local complexity and consider thought-provoking questions in this 49-minute talk by Natalie Frank from Vassar College, presented at the Fields Institute as part of a conference honoring Robert V. Moody's 80th birthday.

Intro
Fibonacci symbolic substitution
Fibonacci natural tile lengths
Cut-and-project scheme
Renormalization for the window
Fibinoid direct product substitution
Fibinoid inflate-and-subdivide rule
A Fibinoid variation
Fibinoid 3D stepped surfaces
Fibonacci direct product substitution
A variation
The measure-theoretic situation
The 28 polygonal windows
Fibonacci DPVs with polygonal windows are topologically conjugate
Rauzy fractal island
Rauzy fractal window comparison
Rauzy fractal castle
Direct products and variations
Park-Robinson 1991: Chacon Z action
A non-Pisot DPV-the symbolic case
A non-Pisot DPV with canonical tiles
Finite local complexity
Some questions