Victor Phan studies mathematical physics at the University of Melbourne in Australia. His early interests in computation brought him to Wolfram Science, and he is considering studying computer science alongside his degree. Victor aims to complete a PhD overseas and found a high-tech research company.
In high school, Victor participated in math and physics competitions and fared well, but he then found doing small research projects much more intellectually rewarding. He likes to write algorithms for his computational experiments and looks forward to doing more experiments in Mathematica.
Victor enjoys composing music on the piano in his spare time and wishes to write orchestral music for cinema or games in the future.
Project: Commutative Cellular Automata
A commutative cellular automaton is a cellular automaton whose rule for determining the value of each cell is independent of the ordering of cells in its neighborhood. For example, the totalistic cellular automata are a well-studied class of commutative cellular automata. In a totalistic cellular automaton, the value of each cell depends only on the sum of the values in its neighborhood. We considered other classes of commutative cellular automata, such as multiplistic cellular automata, where the value of each cell depends only on the product of the values in its neighborhood, and we considered automata where the value of each cell depends only on the sorted sequence of values in its neighborhood. Other operations on the values in the neighborhood can also be considered. We showed that given any commutative cellular automaton, an equivalent totalistic cellular automaton can be found with the same radius and with a specially chosen set of possible cell-values. This is also true for multiplistic cellular automata, and for automata where the value of each cell depends only on the sorted sequence of values in its neighborhood.