# The Lorenz Model - Demo 8

## Sensitive Dependence on Initial Conditions

What happens if we start out the evolution first from one initial condition,
and then from one that differs by a small amount, and compare the two orbits?
We can do this by plotting both trajectories simultaneously on the same plot,
first the *X-Z* projection of the phase space trajectory:

and then directly in the *X(t)* plot:

The two orbits track each other for a considerable time, but even after a quite short
time, are behaving quite differently.

This is the basic conclusion of Lorenz's work: even if you know the initial conditions quite precisely
the error in specifying the initial condition rapidly grows, so that after even a short time we cannot
predict the *details* of the motion - the sensitive dependence on initial conditions that is one
of the defining properties of chaos.

[Previous Demonstration]
[Final Words (pdf)]
[Introduction]

Last modified Thursday, January 6, 2000

Michael Cross