Asynchronous 1D Cellular Automata and the Effects of Fluctuation and Randomness

Cellular automata are used as models of emergent computation and artificial life. They are usually simulated under synchronous and deterministic conditions. Thus, they are evolved without existence of noise, i.e., fluctuation or randomness. However, noise is unavoidable in real world. The target of the present paper is to show the following two effects and several other phenomena caused by existence or nonexistence of noise in the computation order in one-dimensional asynchronous cellular automata (1D-ACA) experimentally. One major effect is that certain properties of 2neighbor 1D-ACA are fully expressed in their patterns if certain level of noise exists, though they are only partially expressed if no noise exists. The patterns generated by 1D-ACA may have characteristics, such as mortality of domains of 1’s or splitting domains of 0’s into two. These characteristics, which are coded in the “chromosome” of the automata, i.e., the look-up table, are fully expressed only when the computation order is random. The other major effect is that phantom phenomena, which almost never occurs in real world, sometimes occur when there is no noise. The characteristics of patterns generated by several 1D-ACA are drastically changed from uniform patterns to patterns with multiple or chaotic phases when only low level of noise is added. Another observed phenomenon is that randomized 1D-ACA generates patterns that are similar to those generated by coupled map lattices (CMLs). This phenomenon suggests that the chaos built into CMLs works similarly to random numbers in 1D-ACA.