Cool looking visualizations are one of the most accessible ways to dip one’s toes into the intersection between mathematics and computer science. Arguably the most iconic of all of these is the Mandelbrot set, and its slightly lesser known cousin the Julia set. For a quick explanation of what they are, and an interactive Mandelbrot and Julia set renderer, click here.

Another interesting area with pretty visualizations is that of cellular automata. These are systems defined on a grid of cells, each of which are in one of many states. The state of each cell evolves over time according to what is typically a set of very simple rules. Despite the simplicity of these rules, complex emergent behaviour often arises. An example of this is Conway’s Game of Life, which you can read more about here.

In the summer of 2021, I also had the opportunity of participating in the Science Summer Research Program at the University of Sydney. My project, supervised by Professor Nalini Joshi, was concerned with studying a certain class of cellular automata called parity filter automata. You can read my final report here.