It’s always interesting to know how great sciences come about, and especially in chaos theory’s case. Arguably one can say that the first glimpse of people becoming aware of chaos came with Aristotle, who observed that
“the least initial deviation from the truth is multiplied later a thousandfold”.
The Complete Works of Aristotle: The Revised Oxford Translation. Princeton University Press.
However, it first sprung into wide-spread recognition during the 1960’s, creating a large scale investigation into the existence of sensitivity dependence. Edward Lorenz accidentally stumbled upon chaos through his work on weather prediction. He was using a simple digital computer to simulate weather and according to a variety of sources he wanted to see a sequence of data at greater length; saving time by starting the simulation in the middle of its path. He returned later to find something quite unexpected; the new printout wasn’t exactly the same as the original printout. Instead, Lorenz saw his weather diverging erratically away from the original pattern, after a few months all similarities disappeared. It wasn’t long until he realised the reason was because of a change in initial conditions. The computer worked to six decimal places, but, the print out rounded to three decimal places. Therefore, instead of .506127, the decimal places .506 were printed.
Lorenz weather printouts, 1961.
To investigate the differences between the two printouts, Lorenz laid both outputs on the same plot. The patterns were initially exactly the same, but as time progressed the patterns diverged, eventually dissipating all similarities. This is when Lorenz discovered that small changes in the initial conditions produced large variations to the outcome of the experiment. This phenomenon is often referred to as sensitive dependence on initial conditions.
So, say we had a system with some variable starting with a value 3, the final outcome could be entirely different with a starting value of 3.0001. This discovery led to the discouragement of long term weather forecasting, and started a new era in science, the chaotic era.