In conversation with a physicist, I learned that the break in a cracked tile exposes where the bond between molecules was weakest. Dropping and breaking a tile is a way of gaining access to its interior structure. If you like to work with the structure of materials, as I do, the inside becomes wide open for investigation.
In this series, one of my first efforts was to draw the largest circle that could fit in each resulting shard. I accepted whatever resulted, rather than reshaping it to conform to a preconception.