What did Lorenz actually change to discover chaos?

He rounded a number. In 1961 Edward Lorenz wanted to re-run part of a weather simulation, and rather than start over he typed in values from a printout - which showed three decimal places where the machine held six. He entered 0.506 instead of 0.506127, expecting a near-identical run, went for coffee, and came back to a completely different weather pattern.

The insight was that this was not a bug. A difference of one part in ten thousand, in a deterministic system with no randomness in it anywhere, had grown until the two runs had nothing in common - which meant that any system of this kind is unpredictable in practice however exactly the rules are known, because the starting state can never be measured exactly.

The butterfly came later and was not originally a butterfly. Lorenz's early talks used a seagull; the title of his 1972 paper - asking whether a butterfly's wings in Brazil could set off a tornado in Texas - was supplied by a colleague when Lorenz failed to provide one in time. The shape of the attractor his equations produce also happens to look like a butterfly, which is a coincidence that has thoroughly confused the story.