Mitchell J. Feigenbaum, a prizewinning physicist and mathematician who was one of the founders of chaos theory, which explores the kind of wildly turbulent, bewilderingly complex systems that defy prediction by standard techniques, died June 30 at a hospital in Manhattan. He was 74.

Dr. Feigenbaum’s death was announced by Rockefeller University in New York, where he continued the work on chaos and associated matters that he had started at Cornell University and at the Los Alamos National Laboratory in New Mexico. The cause of death was a heart attack, said a stepson, Sasha Dobrovolsky.

A mathematical constant that is one of the keystones of chaos theory has been named for him: the Feigenbaum constant. It was revealed as part of his discovery of a powerful and detailed mathematical description of precisely how in a wide array of seemingly disparate systems, order breaks down and makes the transition to chaos.

The constant is a number that gives rise to an endless number of decimal places, but it works out to about 4.6692. The constant, and the equations in which it appears, have been determined to have a widespread applicability across many areas of physics, chemistry and biology. They helped illuminate problems of fluid flow and meteorology.

More than many other abstruse areas of higher mathematics, chaos theory has captured the public imagination. Its allure lies in its recognition that the most infinitesimal changes at the outset can lead almost identical systems into drastically differing directions over time.

Among the best known of these highly sensitive and potentially chaotic systems is the atmospheres, specifically the suggestion that the flapping of a butterfly’s wing in Africa could result in the creation of a dangerous hurricane on the coast of the United States.

But even in the randomness of the routes to disorder taken by so many complex systems, science has found a regularity. Dr. Feigenbaum was regarded as one of the leaders in the effort to find overarching commonalities in how systems become chaotic.

Specifically, in work carried out with Albert J. Libchaber, a Rockefeller University colleague, Dr. Feigenbaum demonstrated the wide applicability of his theory by means of an experiment on fluid dynamics at low temperatures.

This work won for Dr. Feigenbaum and Libchaber the prestigious Wolf Prize in 1986. Dr. Feigenbaum was also a recipient of the MacArthur Foundation award, often known as the “genius grant.”

Mitchell Jay Feigenbaum, whose father was a chemist and mother was a teacher, was born in Philadelphia on Dec. 19, 1944. He showed intellectual gifts at an early age. While classmates dutifully calculated their answers to mathematical problems by use of the figures in tables of logarithms, Dr. Feigenbaum started by computing his own logarithms.

In interviews, he indicated that the presence of a radio in his boyhood home amazed him. He has described his amazement that music could suddenly and regularly issue from an inert device.

After the family moved to Brooklyn, he attended a public high school there. He went on to the City College of New York to pursue his boyhood interest in electricity and studied electrical engineering, receiving a bachelor’s degree in 1964.

In time, he decided the answers to the questions that perpetually engaged him could better be found in physics. He received a doctorate in theoretical physics from the Massachusetts Institute of Technology in 1970.

After postdoctoral work at Cornell and Virginia Tech, he joined the staff at Los Alamos National Laboratory in 1974. He received the Energy Department’s Ernest O. Lawrence Award in 1982, the same year he began working at Cornell. Starting in 1987, he was on the faculty at Rockefeller University and later became director of its Center for Studies in Physics and Biology.

His mathematical gifts, including his grasp of randomness, and his facility with associated geometries, found some outlets beyond pure science. He helped an atlas publisher develop an accurate way of placing portions of the spherical surface of Earth onto a two-dimensional page. He devised means of creating geometric designs on currency that would defy copying or counterfeiting.

His marriages to Cornelia Bibl Dobrovolsky and Gunilla Öhman Wilson ended in divorce. Survivors include two stepsons, Kiril Dobrovolsky of San Francisco and Sasha Dobrovolsky of Nashville; a brother; a sister; and a granddaughter.

Frederick M. Cooper, a PhD physicist who specialized in quantum field theory, said on Medium that of all his friends, Dr. Feigenbaum “was the most unusual and brilliant.”

When he walked through the forest, Cooper said, Dr. Feigenbaum wondered, “At what distance do the trees merge and become inseparable?” When he looked at the moon, he thought, “Why does the moon appear larger when it is on the horizon?”

Then he would develop theories to explain these “from scratch,” Cooper said.