The vascular system of a leaf provides its structure and delivers its nutrients. When you light up that vascular structure with some fluorescent dye and view it using time lapse photography, details begin to emerge that reveal nature's mathematical formula for survival. When it comes to optimizing form with function, it's tough to beat Mother Nature. With support from the National Science Foundation, Rockefeller University mathematical physicist Marcelo Magnasco and his colleague physicist Eleni Katifori analyze the architecture of leaves by finding geometric patterns that link biological structure to function. They study a specific vascular pattern of loops within loops that is found in many leaves going down to the microscopic level. Magnasco says this research is a jumping off point for understanding other systems that branch and rejoin, including everything from river systems, to neural networks and even malignant tumors.