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  • Undergraduate Poster Abstracts
  • FRI-810 SUBSTITUTIONS AND RAUZY FRACTALS

    • Meghan Malachi ;
    • Austin Marstaller ;
    • Jason Saied ;
    • Sara Stover ;
    • Benjamin Itza-Ortiz ;

    FRI-810

    SUBSTITUTIONS AND RAUZY FRACTALS

    Meghan Malachi1, Austin Marstaller2, Jason Saied3, Sara Stover4, Benjamin Itza-Ortiz5.

    1Providence College, Providence, RI, 2The University of Texas at Dallas, Richardson, TX, 3Lafayette College, Easton, PA, 4Mercer University, Martinez, GA, 5Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, MX.

    There exist certain classes of substitutions that can be associated with a geometric representation known as the central tile or the Rauzy fractal. We define 2 distinct, primitive substitutions under a 3-letter alphabet, σ and τ, as having similar Rauzy fractals if their corresponding Rauzy fractals, Tσ and Tτ, respectively, differ by only finitely many points; that is, Tσ is the image of Tτ under a translation. We study specific cases of substitutions under a 3-letter alphabet, A= {a,b,c}, and conjecture that if σn(a) can be described as a permutation of τn(a) for all values of n in the set of natural numbers, then σ and τ have similar Rauzy fractals. We ultimately conjecture that if σ is right conjugate to τ, then σ and τ have similar Rauzy fractals.