  It is shown that the toy Turing Tumble, suitably extended with an infinitely
long game board and unlimited supply of pieces, is Turing-Complete. This is
achieved via direct simulation of a Turing machine. Unlike previously
informally presented constructions, we do not encode the finite control
infinitely many times, we need only one trigger/ball-hopper pair, and we prove
our construction correct. We believe this is the first natural extension of a
marble-based computer that has been shown to be universal.
