An efficient mapping scheme is proposed for embedding any one-dimensional firing squad synchronization algorithm onto 2-D arrays, and some new 2-D synchronization algorithms based on the mapping scheme are presented. The proposed mapping scheme can be readily applied to the design of synchronization algorithms with fault tolerance, algorithms operating on multi-dimensional cellular arrays, and for the generalized case where the general is located at an arbitrary position on the array. A six-state algorithm is developed that can synchronize any m × n rectangular array in 2(m + n) - 4 steps. In addition, we develop a nine-state optimum-time synchronization algorithm on square arrays. We progressively reduce the number of internal states of each cellular automaton on square and rectangular arrays, achieving nine states for a square array and six states for a rectangular array. These are the smallest number of states reported to date for synchronizing rectangular and square arrays.