Andrzej K. Brodzik
One of the main goals of both science and art is to reveal fundamental principles governing space and time. This task can sometimes be facilitated by juxtaposing structure and randomness, intention and accident. Art that explores these relationships in a deep way does not function merely as a pleasing illustration of a mathematical principle, but forms an independent mode of an intellectual interrogation.
Ideal quilts are Zak space representations of families of ideal sequences. Ideal sequences are sequences with certain special group-theoretical properties. In particular, ideal sequences satisfy the Sarwate bound, having both zero out-of-phase autocorrelation and minimum cross-correlation sidelobes. In effect, ideal sequences can be viewed as the quintessential random sequences, or, in the Duchamp language, standard stoppages. For sequence length equal to 7^2 there are exactly 7 sets of ideal sequences. These sequence sets are associated with certain special permutation groups. For further details, see the 2008 Springer book, “Ideal Sequence Design in Time-Frequency Space” by An, Brodzik and Tolimieri, or the forthcoming “Ideal Quilts” by Brodzik.