  The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and
biquadratic interactions and single-ion anisotropy is simulated on a cellular
automaton which improved from the Creutz cellular automaton(CCA) for a simple
cubic lattice. The simulations have been made for several sets of parameters
$K/J$ and $D/J$ in the $-3<D/J\leq 0$ and $-1\leq K/J\leq 0$ parameter regions.
The re-entrant and double re-entrant phase transitions of the BEG model are
determined from the temperature variations of the thermodynamic quantities
($M$, $Q$ and $\chi $). The phase diagrams characterizing phase transitions are
compared with those obtained from other methods.
