Magic squares are n*n square grids in which each row, column, and diagonal add to the same sum. The ‘magic line’, drawn by connecting each integer in numerical sequence, creates a pattern that can differ or be shared between instances. The dual purpose of this work is: 1. to produce a variety of artworks—printed, digital and animated that use the magic line as a departure point; and 2. to investigate mathematical processes (matrix transformations) that produce identical magic line patterns, with the aim of identifying all unique such patterns, and simplifying the classification of magic squares, using visual and programmatic methods. The ongoing creative process has led us to produce a web-based visualisation tool (squares.cubelife.org), with which we have explored different types of mathematical curve to visualise the magic line, and to identify certain useful groups. This can already produce an extensive variety of interesting aesthetic results that differ from existing ‘straight line’ visualisations of magic squares. As well as exploring the creative visual permutations, our methods also enable the measurement of certain properties, such as the length of the magic line and the results of certain transformations.