**Student Research Projects**

**Undergraduate**

The 2007 REU team, composed of Michael Cantrell and Robert
Price, completed the project "Self-intersection properties of generalized Koch
curves." The students presented their results at the joint AMS/MAA meetings

The 2006 REU team, composed of Rebecca Black, Phil Hudelson,
Lisa Lackney and Jim Rohal, completed the project "Self-similar
tilings
of nilpotent Lie groups." Jeff
Adler was co-director of this project. The students presented their results at
the joint AMS/MAA meetings in

Naomi Cummings Ducharme, a mathematics and secondary education major, completed an honors project on Penrose tilings.

Rebecca Brown, an applied mathematics major, completed an honors project
entitled "Fractal
Tilings
in the Plane." Rebecca developed the necessary and sufficient conditions for a
2 x 2 matrix to be used to generate fractal
tilings
of the plane. The original 2 x 2 matrix *M* must be an integer matrix, but
it may undergo a transformation (multiplication by a transformation matrix) in
order to generate the desired tiling. Rebecca presented her results at the
Research by Undergraduates poster session at the AMS/MAA meetings in

Sara
Hagey, an applied mathematics major, completed an
honors project entitled "Fractal
tilings
derived from complex bases." Sara studied the radix expansion of complex
numbers in complex bases. She then used iterated function systems derived from
the complex base to generate a tiling of the plane. Her paper explains the
relationship between the radix expansions and the
tilings
generated. Sara presented her results at the Research by Undergraduates poster
session at the AMS/MAA meetings in

Jennifer
Schenkenberger,
a
mathematics
major with emphasis in education, completed a project to introduce fractal
geometry into the secondary classroom. She has developed a collection of units
on the chaos game, iterated function systems, the random iteration algorithm
and other topics in fractals.

Matthew
Palmer participated in a summer research program at the

Maria
Salcedo, a student at

**Graduates**

Mary Knust completed a thesis on "Integration on Fractals" where she developed a trapezoidal-type method for approximating integrals over fractal regions.

Samantha Fales completed a project on "Random Sierpinski Triangles" where she introduced elements of randomness into the construction of the Sierpinski Triangle.

Cathy Miller completed a project on "The Hausdorff metric and Julia sets." Cathy did a thorough study of the completeness of the Hausdorff metric and the application of that in the convergence of fractals. She also looked at the properties of Julia sets and the Mandelbrot set.