Let's look more specifically at the mathematics behind Edward Lorenz's discovery. In the program that he ran, it is a program of 3 differential equations with respect to time: x is proportional to the rate of convection, y to the horizonatal temperature variation, and z to the vertical temperature variation. The equations would later be called the Lorenz equations. Later, scientists Robert Shaw and Peter Scott at the University of California in 1977 used an older machine at the time called an analog computer. Turning the Lorenz equations into electrical circuitry or simply a large amount of wires to represent the 3 equations such that the voltage that comes out of the system is the answer to the equation (Chaos Theory PBS). Resulting in what we call today, the Lorenz Attractor.
With a look of a butterfly's wings, this showed that something that is a chaotic system can also be a system of order.
"Traditionally, the changing values of any one variable could be displayed in a so-called time series[...]. To show the changing relationships among three variables required a different technique. At an instant in time, the three variables fix the location of a point in three-dimensional space; as the system changes, the motion of the point represents the continuously changing variables. Because the system never exactly repeats itself, the trajectory never intersects itself. Instead it loops around and around forever. Motion on the attractor is abstract, but it conveys the flavor of the motion of the real system. For example, the crossover from one wing of the attractor to the other corresponds to a reversal in the direction of spin of the waterwheel or convecting fluid" (Gleick, 29).