  Surfaces sputtered by ion beam bombardment have been known to exhibit
patterns whose behavior is modeled with stochastic partial differential
equations. However, we apply a new approach by the use of the famous Lorentz
equations to simulate and predict such patterns. It has been earlier reported
that at early times, during sputtering, surface displays a chaotic pattern,
with stable domains that nucleate and grow linearly in time until ripples
domains of two different orientations are formed. The numerical solutions of
the Lorentz model, being an unstable and chaotic model, give a pattern similar
to modern surface evolution simulations. The ultimate goal was to predict the
most common surface morphology by constantly varying the parameters of the
Lorentz model and study the effects on the simulated surface patterns. Almost
all of the recent experimentally observed and theoretically predicted
formations are accurately obtainable with this concept.
