These pictures from my collection have been taken over the last several years in a variety of locations both within and outside the U.S. Every pattern you see has an underlying mathematical description, at least in part, and frequently an explanation (even if we don't know what it is yet!). I believe fervently in enjoying and sharing "the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature"; I hope that you enjoy them also! Mathematics reveals the poetry of nature. More about the mathematical modeling of nature can be found in the "Books" section of this site.
If you wish to use any of these pictures, please email me at firstname.lastname@example.org describing the context in which you wish to use them.