Sequential Binary Arrays. I. The Square Grid

A periodic binary array is said to be sequential if and only if every line of the array is occupied by a given periodic binary sequence or by some cyclic shift or reversal of this sequence. Such arrays are of interest in connection with experimental layouts. This paper, which deals only with arrays built on the square grid, gives some constructions for sequential arrays and some results on the types of arrays possible for certain sequences. The x-step circulant arays are characterized. A technique for exhaustive search to find all possible arrays with a given sequence is outlined and a listing is given for square sequential arrays of period not exceeding seven.