SUBSTITUTIONS AND SIMILAR RAUZY FRACTALS
Austin Marstaller1, Meghan Malachi2.
1The University of Texas at Dallas, Richardson, TX, 2Providence College, Providence, RI.
Let A be an alphabet and let S and T be substitutions under A. There exist certain classes of substitutions that can be delineated by a fractal, specifically a Rauzy fractal. We attempted to characterize substitutions over a 3-letter alphabet that produce Rauzy fractals that are translations of one another. The methods we employed were analyzing the "staircase" constructed from the sequences created by the substitutions as well as thoroughly examining the structure of those sequences. Through these methods, we have found that should a substitution be right-conjugate to another, they will generate Rauzy fractals which are translations of one another. In future research, we wish to find more interesting characteristics of substitutions which generate similar Rauzy fractals.