James Gleick (American author and historical scientist) has written a very interesting book on the field known as "
chaos theory" - a sensitive dependency on initial conditions. The field was accidentally discovered by the young French mathematician Henri Poincaré while attempting to find an exact mathematical solution for the three body problem.
Lorentz, in the weather field, rediscovered this idea and provided a name for it. The
analogy is that, due to round-off errors in computations, it is "
as if" a butterfly flapped it's wings in California and a typhoon resulted in China.
Gleick, J. (1988).
Chaos: making a new science. New York: Penguin Books..