Wolfram Computation Meets Knowledge

Wolfram Summer School


Kate Morrow

Summer School

Class of 2007


I’m currently an undergradute student at the University of Vermont (UVM), and will be returning for my final semester this fall. I’m pursuing degrees in both physics and mathematics, and am planning on graduate school next fall in theoretical/mathematical physics. My academic interests are not limited to these subjects, however. I have been a musician for most of my life and am always eager for a chance to improve my periodically rusty French. I’m also very interested in the history and philosophy of many Eastern religions, particularly Daoism and Ch’an/Zen Buddhism. I attended Middlebury College from 2002 to 2005, where I studied physics and music, before taking a year and a half off from school and returning to academics at UVM this past January.

Project: Dynamic Structure in Networks: A NKS Approach

Networks with structure updated according to simple rules is a piece of the NKS computational universe which has not yet been thoroughly explored. (See NKS, pgs. 193-203) My project is an attempt to begin examining these programs in more detail.

Network structure update rules were defined and enumerated for distances one and two. An exhaustive search was conducted of the distance-one rules, which resulted in exclusively simple behavior. A random search was then conducted of over 23,000 distance-two rules. A much more diverse variety of behavior was seen in these rules, and eight of the searched rules appeared to exhibit complex behavior.

The update rules of distance-two were observed to be above the threshold of complexity for this type of simple program. A variety of interesting and surprising population behavior was found. The actual network structure was examined for some of the more interesting rules, suggesting underlying properties of catastrophic behavior, and avenues for further investigation.

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 4696290

I chose this rule because of its consistency through my repeated attempts at making it do something different. I decided that I appreciated its resilience, and how it represents that stability can be found in unexpected places.