As a braidmaker, my work encompasses both maths and art. However, language can be a bridge, or a barrier, between different disciplines and without a 'mathematical language' it has been difficult for me to access work done in this field. This paper describes my search for a visual language that provides me with a practical and theoretical way of comparing and analysing braid structure. From this comes the means of discovering all possible braid structures for a set of given constraints. Although braids have been made for millennia, they tend to be limited to certain types of structure. These have usually evolved from the characteristics found within the methods of production. Approaching the subject from a mathematical viewpoint, enables me to find new structures from the wealth of possibilities that have yet to be explored.