Math REU groups from Amherst College, Tufts University, UConn, UMass and Yale University are getting together online on Thursday July 29th for a conference to share their summer research work. Check out the 2021 Math REU conference website
Geodesics (shortest paths) on manifolds such as planes and spheres are well understood. Geodesics on fractal sets such as the Sierpinski Triangle are much more complicated. We begin by constructing algorithms for building shortest paths and provide explicit formulas for computing their lengths. We then turn to the question of interpolation along geodesics—given two subsets of the Sierpinski Triangle, we “slide” points in one set along geodesics to the other set. We construct a measure along the interpolated sets which formalizes a notion of the interpolation of a distribution of mass, and we prove interesting self-similarity relations about this measure.
Publication: J. Fractal Geom. 8 (2021), 117-152 doi.org/10.4171/JFG/100 arXiv:1912.06698