Tara Taylor's

Research

There are many things that interest me, and so my background is quite diverse.  My current research focuses on fractals and topology.  One ongoing project is an investigation of the topological properties of the Sierpinski relatives, a class of fractals that all have the same fractal dimension but different topologies.  Another class of fractals that interests me are fractal trees.  

As an undergraduate student at the University of Winnipeg, I did some work in the area of algebraic graph theory with Dr. William Martin.  For my master's degree at Dalhousie, I worked with Dr. Alan Coley in cosmology.  My master's thesis involved the analysis of cosmological models with dynamical systems.  In May 2005, I successfully defended my PhD thesis "Computational Topology and Fractal Trees" (see below for a link to the thesis), so my current research involves an analysis of fractal trees using methods of computational topology.  My supervisor was Dr. Dorette Pronk of Dalhousie University.

Topology

Topology is a vast, beautiful field in mathematics.  Topology involves a type of geometry that ignores concrete spatial notions such as straightness, convexity and distance, and considers properties such as connectivity, orientability and continuity.  To a topologist, a donut is equivalent to a coffee cup. Topology Links

Fractals

Fractals can be used for many different applications, such as the study of river drainage systems, the branching of cardiovascular systems, the distribution of forest growth.  There is no specific definition of fractal, but they generally exhibit properties like self-similarity and detail at arbitrary scales.  My current work focuses on the class of fractals known as the Sierpinski Relatives.  This class includes the well-known Sierpinski gasket, and the others are obtained by using symmetries of the square.  A sample are shown below.

The Golden Ratio

The golden ratio is a fascinating number that has many interesting properties, including a connection to self-contacting trees that I discovered during my thesis work.  The fractal tree shown at the top of this page scales according to the golden ratio.  Golden Ratio Links

Sample Publications

Selected Talks/Posters (needs to be updated)

last updated June 12, 2013