Mitchell J. Feigenbaum, a pioneer in the field of mathematical physics known as chaos, died June 30 in Manhattan. He was 74.

At Los Alamos National Laboratory in New Mexico in the mid-1970s, Dr. Feigenbaum, using a programmable calculator, found what seemed at first a mathematical curiosity. A simple equation generated a sequence of numbers which were initially trivial: the same number over and over. But as a parameter in the equation shifted, the output became more varied. First, the numbers bounced back and forth between two values, then they cycled among four values, then eight, and so on, with the rate of the change quickening until the patterns lost repeating cycles.

The dynamics had, in the terminology of physics, passed into the realm of deterministic chaos. That is, each number of the sequence could be computed precisely, but the resulting pattern appeared to be complex and random. He calculated the rate of that quality, known as doubling, and found that it occurred about 4,669 times as quickly as the previous one. That number is now known as the Feigenbaum constant, a universal mathematical constant, like pi.