# Briana McGarry

Summer School

Class of 2006

## Bio

Briana McGarry is currently working on a bachelor of science in mathematics at Central Michigan University (CMU). She has an interest in cryptography and number theory. Last summer, she did a research project at CMU dealing with cellular automata and its possible application to encryption. Briana presented her findings at the undergraduate conference at Ohio State University, the fall Midwest NKS conference, and the joint mathematics conference in San Antonio, Texas. Briana also enjoys playing piccolo in the CMU marching band, swimming, playing ultimate frisbee, playing disc golf, and collecting rubber ducks!

## Project: Turing Machines through State-Transition Diagrams

I am looking at two-color, two-state Turing machines on a finite tape. The finiteness of the tape implies that the tape wraps around, making the left neighbor of the leftmost bit the rightmost bit, and the right neighbor of the rightmost bit the leftmost bit.

Because only a finite number of possibilities thus exist, the state-transition diagrams will therefore terminate in cycles. I am going to try to track these and look for patterns.

## Favorite Four-Color, Radius-1/2 Rule

Rule chosen: 1000053

This is rule 1000053. I like it because the repitition makes it appear as if there is a light up in the corner. If every other row is taken, one can fully see the how the colors grow. The slope of the top line is -1 while the slope of the bottom line is -2. Another pattern that can be found in this CA is on the diagonal: every 6 lines, the CA picks up another diagonal section that repeats.

• 22nd Annual Wolfram Summer School
• Bentley University, Waltham, MA, USA
• June 23–July 11, 2024