Wolfram Computation Meets Knowledge

Wolfram Summer School


Sarah Flannery

Summer School

Class of 2003


In June 2003 Sarah gained a BA in Computer Science from the University of Cambridge, UK. In 1999 she was a winner of both the Irish and, later, European Young Scientist of the Year for work on Cryptography. The following year the popular-science bestseller In Code: A Mathematical Journey, written with her father David, was published at the request of Profile Books Ltd., London. At present she is working for Wolfram Research.

Project: An Investigation of Cellular Automaton Rule Number 699927 and other distractions!

Initially the focus of the project was to meet the task of investigating the properties of Cellular Automaton, such as rule 30, which make them suitable candidates for use in cryptographic schemes. In the final week of the summer school, however, efforts were fully devoted to exploring what could be achieved in a short study of a particular Cellular Automaton, chosen for its similarity in evolution to Rule 110 and thus, the possibility that it would lend itself to a universality proof. This likeness showed itself in the persistent structures observed, and the ‘interactions’ between them. However, in Rule 699927 interactions, structures and background patterns are expressible in much shorter form than is possible with Rule 30. The goal of this aspect of the project then was to represent structures in the rule using a suitable scheme. With the collection of ‘operations’ built up in that way experiments were carried out to construct ‘programs’ to emulate the operation of NAND gates and a repository of ‘functions’ necessary to begin a universality proof of the type used for Rule 110 in which cyclic tag systems are emulated.

Favorite Three-Color Cellular Automaton

Rule Chosen: 6999927

Reason: I began by choosing 3-colour CA at random and came across this one, noticed the beginnings of the horizontal and diagonal structures that prompted me to iterate the CA further to see what happened at their intersection… and I wasn’t disappointed.

When really interesting structures appear as a result of visually almost imperceivably small changes in the ‘background’ the pattern was identified and coloured red and blue–this little {2,0,0,2} pattern causes some of the most interesting structures to be formed.