Dr. Art Winfree

Art Winfree, who combined insights from mathematics and the life sciences to illuminate the workings of nature ' s biological rhythms, died Nov. 5 in Tucson, where he was a professor at the University of Arizona. He was 60.

The cause was a brain tumor, his colleagues and family said.

Dr. Winfree was a pioneer in understanding the phenomenon of self-organization: how large groups of biological " oscillators, " including blinking fireflies, chirping crickets and pulsating heart and brain cells, spontaneously become synchronized, beating in unison. He also demonstrated how even the most robust of these rhythms can collapse, giving rise to chaotic gyrations, which can have fatal consequences.

With implications for both mathematics and medicine, his work was honored with both the Norbert Wiener Prize in Applied Mathematics in 2000 and the Einthoven Award in Cardiology in 1989. When he was 42 and a professor at Purdue University, he received a MacArthur " genius " grant, awarded to " exceptionally talented individuals. "

" Art Winfree has changed the way we think about several entire subfields of science, " wrote Steven H. Strogatz of Cornell, in nominating his former mentor for the Wiener Prize. " His brilliant intuitions have repeatedly opened new fields of mathematical inquiry. "

Arthur Taylor Winfree was born at St Petersburg, Fla., on May 15, 1942. After earning a bachelor ' s degree in engineering physics from Cornell University in 1965, he gravitated toward theoretical biology, a small field that seeks the mathematical underpinnings of living processes.

Wiener, who established cybernetics, the study of how complex systems regulate themselves, had himself tried to explain the mysterious origins of biological rhythms. A breakthrough came in a paper Dr. Winfree published in 1967 when he was a graduate student at Princeton.

Describing how thousands of cells beating at different paces could coordinate their behavior was a daunting prospect. But Dr. Winfree cut through the detail, showing that, as the differences in the cells ' frequencies are reduced, they abruptly fall into lockstep. They undergo what scientists call a phase transition, as when water freezes into ice.

He went on to show how fragile these ensembles could be. And he used ideas from topology, the mathematics of shapes and surfaces, to make a surprising prediction: that under the right conditions, even a slight disturbance could cause the beating to stop.

Dr. Winfree earned his Ph.D. from Princeton in 1970 by demonstrating the phenomenon in experiments involving the circadian rhythms of fruit flies. Working at the University of Chicago, Purdue and finally Arizona, he took on more complex patterns, showing that rotating spiral waves could spontaneously arise in dishes of chemicals. These self-sustaining gyres are now believed to be associated with heart arrhythmias.

Many of his ideas are described in his book " The Geometry of Biological Time " (Springer Verlag), which was published in 1980 and revised in 2001.

Dr. Winfree was something of a scientific loner, rarely collaborating on a paper. " He loved doing it by himself, " Strogatz said. " He could also be hard to work with. He was one of those people who didn ' t feel a need to sugar-coat his opinions. He just wanted to get to the truth. "

In recent years, his best-known class at Arizona was the Art of Scientific Discovery, an effort to teach students to think creatively. Hard problems, Dr. Winfree said in the syllabus, are " the equivalent of barbells for lifting. "

In Adventures in Discovery, a column he wrote for the Society of Amateur Scientists, he described the kind of everyday puzzle he found so fascinating. One night, he noticed that when the fluorescent-lighted globes outside his house automatically switched on, they seemed to crawl with " vaguely patterned purple blotches that shift and flicker, separated by yellow worms like electrical discharges that squirm around. "

After experimenting with pulsing lights, an oscilloscope and his own perceptions, he tentatively concluded that the phenomenon existed not with the lamp but in the effect of its flickering on the human brain. He went on to speculate about what this might say about neural functioning.

Strogatz said this was classic Winfree: " He would pose problems for himself without even caring whether they had a solution. "

He is survived by his wife, Ji-Yun Yang, whom he married in 1983; a daughter and son from a previous marriage, Rachael Winfree, a researcher in the department of ecology and evolutionary biology at Princeton, and Erik Winfree, an assistant professor of computer science, computation and neural systems at the California Institute of Technology; his father, C. Van Winfree; a sister, Phyllis Laidre; and two brothers, Charlie and Robert.