Though I'm a nonmathematician, the intuitions my work originates in have consistently led to an art of visual mathematics. Such an art obviously has a special resonance for scientists and mathematicians, but being visual, it can be just as immediately engaging for general audiences. Its patterns invite mathematical analysis, but require none, and need only be seen as music need only be heard. The critical measure of their success is the degree to which they are reminiscent of the deep mathematical coherencies found in the forms and dynamics of nature, but again no analysis is necessary for this recognition to be implicitly felt as an aesthetic intuition. In other words, when successful, this art bears a relation to the natural world similar to that of the best pure mathematics where eventually an application is always found. It is after all mathematics as a form of visual aesthetics.