Paths in Fractals generated by pairs of geometric similarities
By: Nicholas C Mendler
Department: Mathematics
Faculty Advisor: Dr. Chun-Kit Lai
Topological, measure theoretic and geometric properties of the attractors of second order similitude iterated function systems are investigated. Theory and algorithms are developed for determining connectedness and dimension. Restricted iterated function systems are introduced to generate geometrically significant paths in the attractor, and theory is developed for the measurement of the similarity dimension of the introduced paths.