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 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.
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
"Mat Weaving: Towards the Mobius Strip", By Eva Knoll, Wendy Landry, and Tara
Taylor, to appear in the Proceedings of the Bridges Enschede 2013 Conference
Mathematics, Music, Art, Architecture, Culture.
"Examples of Using Binary Cantor Sets to Study the Connectivity of Sierpinski
Relatives", by T.D. Taylor, C. Hudson and A. Anderson, in Fractals,
Volume 20, Number 1, pages 61-75, 2012.
"Connectivity Properties of Sierpinski Relatives", by T.D. Taylor, in
Fractals, Volume 19, Number 4, pages 481-506, 2011.
'"Excursions through a Forest of Golden Fractal Trees", by
T.D. Taylor, in The Beauty of Fractals: 6 Different Views, eds. Denny
Gulick and Jon Scott, Mathematical
Association of America, 2010.
"A New Classification of Non-overlapping Symmetric Binary Fractal Trees Using
Epsilon Hulls", by T.D. Taylor, Volume 17, Fractals, 365-384, 2009.
"Topological Bar-codes of Fractals", by Tara D. Taylor, Volume 84 (Convex
and Fractal Geometry), Banach
Center Publications, 181-222, 2009
"Thin Sets with Fat Shadows: Projections of Cantor Sets" by F. Mendivil and T.D.
Taylor, Volume 115, The American Mathematical Monthly, 451-456, 2008.
"Homeomorphism Classes of Self-contacting Symmetric Binary Fractal Trees'', by
Tara D. Taylor, in Fractals, Volume 15, Number 1, pages 9-25, 2007.
- PhD Thesis: "Computational
Topology and Fractal Trees"
- "Self-similar Spherically
Symmetric Cosmological Models With Two Scalar Fields" (
and Quantum Gravity (18), 2001,
- "A Grad Student at the
Laval Meeting" (Canadian Mathematical Society Notes, Volume 34,
number 5, September 2002). To view this article, click
and turn to page 18
Selected Talks/Posters (needs to be
"Totally Disconnected Sierpinski Relatives", talk at the
CMS Summer Meeting, Halifax, June 2013.
"Golden Fractal Trees", talk at the Bridges Conference
(Mathematical Connections in Art, Music and Science), San Sebastian/Donostia,
Spain, July 2007
"Topological Barcodes of Fractals", talk at Convex and
Fractal Geometry Conference, Bedlewo, Poland, May 2007.
"Finding Gold in the Forest: Fractal Trees and the Golden
Ratio", Joint Meeting of the American Mathematical Society and the Mathematical
Association of America, New Orleans, January 2007.
"New Classifications and Characterizations of Fractal Trees Using Methods of
Computational Topology", poster at FRACTAL 2006, Vienna, Austria, February 2006.
"Finding Gold In The Forest...A Connection
Between Fractal Trees, Computational Topology and The Golden Ratio"
"Butterflies and Mathematics"
at the Dalhousie Honours Math Seminar, November 19. 2003. Click
to see the slides (but only the text part)
"Fractals in Nature"
at the Dalhousie Honours Math Seminar, February 26, 2003. Click
to see the slides (only the text part, unfortunately no pictures)
"An Introduction to the Axiom of Choice" at
the Dalhousie Graduate Student Seminar, January 31, 2003. Click
to see the slides
last updated June 12, 2013