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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA

Alumni

Jesse Nochella

Class of 2006

Bio

Jesse Nochella is a high school student from New Sharon, Maine. For the past two years he has been active on the NKS Forum, asking questions, and performing NKS experiments. When he is not working on his computer or talking about NKS, he has been busy with extracurricular activities including robotics, theater, canoeing, civic volunteering, and snowboarding.

Project: Path-Rewriting Cellular Automata

Ordinary cellular automaton systems have the constraint in their construction that they cannot change the topology of the network they operate on while they evolve. The idea of this constraint being removed is considered here in the simplest of cases.

So-called path-rewriting cellular automata were constructed to investigate a type of cellular automaton that uses the sequence obtained in its neighborhood and, in addition to changing its own color, chooses a new neighborhood as well for the next step. A simple possibility space was investigated and analyzed.

Path-rewriting cellular automata evolve in the following fashion:

Every system operates on a network where each node has one state and one outgoing connection. At each step, each node looks at the states of the nodes following successive connections ahead of it. The nodes then use these states to decide two things: the new state of the node, and which "downstream" node it will connect to.

The rule icon here shows what a node will do with a particular sequence. The leftmost cell is the node itself, and there are two downstream connections. A cell in the top center means that the node stays connected to the one it's already connected with, while a top right cell means that the node has jumped to the next connection.

Project-Related Demonstrations

View demonstration of Wolfram Demonstrations Project

Favorite Four-Color, Radius-1/2 Rule

Rule chosen: 2099818467

Rule 2099818467 from a single black cell on an infinite white background produces an interesting pattern that can be seen clearly by looking at every other cell horizontally and vertically. It forms regions that are nested inside of each other and develop, grow, shrink, and merge together in a random fashion.

In a finite space with random initial conditions, all background patterns eventually converge to one single pattern with about a 50/50 probability of it being the "white" pattern or the "black" one.