  The Collatz, or 3x+1, Conjecture claims that for every positive integer n,
there exists some k such that T^k(n)=1, where T is the Collatz map. We present
three cellular automata (CA) that transform the global problem of mimicking the
Collatz map in bases 2, 3, and 4 into a local one of transforming the digits of
iterates. The CAs streamline computation first by bypassing calculation of
certain parts of trajectories: the binary CA bypasses division by two
altogether. In addition, they allow for multiple trajectories to be calculated
simultaneously, representing both a significant improvement upon existing
sequential methods of computing the Collatz map and a demonstration of the
efficacy of using a massively parallel approach with cellular automata to
tackle iterative problems like the Collatz Conjecture.
