  We study a cellular automaton model, which allows diffusion of energy (or
equivalently any other physical quantities such as mass of a particular
compound) at every lattice site after each timestep. Unit amount of energy is
randomly added onto a site. Whenever the local energy content of a site reaches
a fixed threshold $E_{c1}$, energy will be dissipated. Dissipation of energy
propagates to the neighboring sites provided that the energy contents of those
sites are greater than or equal to another fixed threshold $E_{c2} (\leq
E_{c1})$. Under such dynamics, the system evolves into three different types of
states depending on the values of $E_{c1}$ and $E_{c2}$ as reflected in their
dissipation size distributions, namely: localized peaks, power laws, or
exponential laws. This model is able to describe the behaviors of various
physical systems including the statistics of burst sizes and burst rates in
type-I X-ray bursters. Comparisons between our model and the famous forest-fire
model (FFM) are made.
