  Sand pile formation is often used to describe stratified chaos in dynamic
systems due to self-emergent and scale invariant behaviour. Cellular automata
(Bak-Tang-Wiesenfeld model) are often used to describe chaotic behaviour, as
simulating physical interactions between individual particles is
computationally demanding. In this study, we use a state-of-the-art parallel
implementation of the discrete element method on the graphical processing unit
to simulate sand pile formation. Interactions between individual grains were
simulated using a contact model in an Euler integration scheme. Results show
non-linear self-emergent behaviour which is in good agreement with experimental
results, theoretical work and self organized criticality (SOC) approaches.
Moreover, it was found that the fully deterministic model, where the position
and forces on every individual particle can be determined every iteration has a
brown noise signal in the x and y direction, where the signal is the z
direction is closer to a white noise spectrum.
