The demonstration shows a graphical representation of the time variation of three variables X(t),Y(t) and Z(t), coupled by non-linear evolution equations.... This tiny difference in the initial conditions becomes amplified by the evolution, until the two trajectories evolve quite separately. The amplification is exponential, the difference grows very rapidly and after a surprisingly short time the two solutions behave quite differently. This is an illustration of the butterfly effect - the idea in meteorology that the flapping of a butterfly's wing will create a disturbance that in the chaotic motion of the atmosphere will become amplified eventually to change the large scale atmospheric motion, so that the long term behavior becomes impossible to forecast.