On the abundance of traveling waves in 1D infinite cellular automata

✍ Scribed by Maurice Courbage

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 635 KB
• Volume: 103
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00256-4

✦ Synopsis

The waves we study are the analog of traveling waves u (x, t) = H (x + v t), where x represents the space vailable, t the time and v the velocity. Here we consider the simplest waves generated by the configurations (ui) : u(i, t) = (Otu)i, i c Z, ui E {0, 1 ..... k -1}, where 0 is the deterministic dynamics of cellular automata on the configuration space. We study intial configurations which evolve as spatially periodic waves under rule 90. The wavelength distribution for different velocities of propagation is reduced to an eigenvalue problem of a class of matrices in finite fields. We show that the set of the wavelengths is unbounded.