  We present highly accurate Monte Carlo results for simple cubic Ising
lattices containing up to $256^3$ spins. These results were obtained by means
of the Cluster Processor, a newly built special-purpose computer for the Wolff
cluster simulation of the 3D Ising model. We find that the magnetization $M(t)$
is perfectly described by $M(t)=(a_0-a_1 t^{\theta} - a_2 t) t^{\beta} $, where
$t=(T_{\rm c}-T)/T_{\rm c}$, in a wide temperature range $0.0005 < t < 0.26 $.
If there exist corrections to scaling with higher powers of $t$, they are very
small. The magnetization exponent is determined as $\beta=0.3269$ (6). An
analysis of the magnetization distribution near criticality yields a new
determination of the critical point: $K_{\rm c}=J/k_B T_{\rm c}=0.2216544$,
with a standard deviation of $3\cdot 10^{-7}$.
