Bio

Anthony Joseph is a student at the University of Technology, Sydney, in New South Wales, Australia. He is currently in his fourth year in a combined software engineering and mathematics degree. He began his undergraduate studies at University of Technology, Sydney as an engineering cooperative scholar. Anthony has worked for both commercial enterprises and research organizations within New South Wales in a software engineering and a mathematics context. His interest in a New Kind of Science was sparked after completing a software engineering class which involved the use of tools such as Turing machines and automata to define software functionality. He intends to discover new and exciting applications of a New Kind of Science in software engineering.

Project: Register Machines – An Analysis of Complex and Random Behaviour and Functionality

Register machines are logical abstractions of registers used in digital electronics – from microcontrollers to personal computers. A register machine is comprised of a program based on a defined instruction set, a program counter, and a set of registers of various widths at a defined initial state. To discover various functionalities, these parameters will be altered. Although register machines have been investigated between the 1940s to the 1970’s and in Wolfram’s A New Kind of Science, this investigation will focus on discovering and classifying various register machines and defining machine capabilities. Basic register machine functionality involving manipulating variables stored in one or several registers will be defined as well as identifying equivalent and inequivalent functions, and functions that have deterministic halting, or functions that continue indefinitely.

Project-Related Demonstrations

Planar Trivalent Network Growth Using Two Rewrite Rules

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 3226576

ArrayPlot[CellularAutomaton[{3226576, {3, {3, 1, 3}}}, {{1}, 0}, 100], ColorRules -> {0 -> LightBlue, 1 -> Blue, 2 -> Cyan}]

For the outer totalistic automata my favorite rule is 3226576. It appears to emulate the behaviour of a rule-90 cellular automaton but is capable of altering the inner background pattern by rotating 90 degrees. It also appears to be symmetric and contain non-standard inner structures.