We identify some desired mathematical properties of bonds in an Artificial Chemistry (AChem) that promote complexity and open-ended behaviour (i.e. an AChem not designed to display particular behaviours). We identify the underlying structures created by different properties of mathematical products. We use these to exploit existing algebra to generate a potentially open-ended subsymbolic AChem (ssAChem). We give examples of how our approach leads to interesting behaviour, focused on the structure of composite particles within our system.