To understand the Butterfly Effect, one must understand the difference between a linear and a nonlinear system. In a linear system, the output is proportional to the input; if you push a swing twice as hard, it goes twice as high. However, most of the natural world is nonlinear.
Lorenz assumed that a tiny difference—one part in a thousand—would have a negligible impact. Instead, the new weather pattern diverged completely from the original. Within a short period, the two simulations looked nothing alike. This led to his realization that complex systems are characterized by "sensitive dependence on initial conditions." Complexity and Chaos The Butterfly Effect