  Geometrical Computation as a new model of computation is the counterpart of
Cellular Automata that has Turing computing ability. In this paper we provide
an algorithm to simulate Alternating Turing Machine in the context of Signal
Machine using techniques adopted from the features of Signal Machine to set up
and manage the copies/branches of Alternating Turing Machine. We show that our
algorithm can simulate Alternating Turing Machine in Signal Machine as same
functionality as classic family of Turing Machines. Time complexity of the
algorithm is linear as ordinary simulated Turing Machines. Depending on the
computation tree space complexity is exponential order of d, where d is the
depth of the computation tree.
