## Student Profile: Antony Kennett

#### Biography

Antony has recently completed his fifth year studying at Monash University, currently enrolled in a double degree of a Bachelor of Science (majoring in Applied Mathematics) and Bachelor of Laws. In addition to studying, he also tutors high school mathematics, and works in quantitative analytics at a sports betting start up. He intends to pursue a mathematic-based career after finishing his degree.

#### The Percolation of Cellular Automata

Consider the following self-organised system on N×N. The vertices are labelled using the familiar euclidean coordinates. To each vertex we assign a value in {−1,1} according to the following rule. The value at vertex (i,j) is the product of the values at (i,j−1) and (i−1,j). The system is well deﬁned once we provide the boundary conditions, which are the following. The vertices with coordinates (1,j), with j ≥ 1 have all the same value. The values of the vertices of the form (i,1), with i ≥ 1 are generated at random according to a certain rule. This project investigates the main features of this system.