Graphing a Rubik's Cube in Music

The connections between the Rubik’s Cube, group theory, and Cayley graphs is explored. It provides a comprehensive introduction to these concepts and their relation. The Rubik’s Cube is a popular puzzle, and the collection of all its possible states constitutes a group under face rotation operations. Focusing on the Rubik’s Cube group, we delve into the mathematical structure underlying this puzzle’s structure. A key object of this exploration is the Cayley graph, which visually represents the Rubik’s Cube group. This graph connects the Rubik’s Cube with many other topics and lead to many applications. By modeling the Rubik’s Cube as a random walk on its corresponding Cayley graph, we gain insights into scrambling and solving processes. Another surprising application is its connection to musical patterns through modulation graphs. This paper aims to bridge the gap between abstract algebraic concepts and their tangible applications in the Rubik’s Cube.