6. Conclusions

The effects of adding randomness, fluctuation or noise in the order of computation in 1D-ACA is separated from those caused by asynchronity by comparing randomized and interlaced versions of the automata. Two major effects of randomness in 1D-ACA are shown in the present paper.

One major effect of randomness is that properties of 1D-ACA, which are embedded in their ``chromosomes'' only in the case of asynchronous automata, are fully expressed in their patterns when stronger noise exists, i.e., when the order of computation is random. However, the properties are only partially expressed when no noise or weaker noise exists.

The other major effect is that very fragile particles and domains, which may probably be regarded as phantom phenomena because they are almost never seen if noise exists, are sometimes observed in noise-less environments (in Sections 3.4 and 4). The characteristics of patterns generated by several 1D-ACA are drastically changed from uniform patterns to patterns with multiple or chaotic domains even if low level of randomness is added. Several other effects, such as delay of pattern motion under existence of noise, which is partially mentioned by Ingerson and Buvel [Ing 84], are also observed. Although 1D-ACA are simpler systems, I believe the results of this research contribute to research of emergent computation, such as CCM (chemical casting model) [Kan 94], and artificial life.

One important direction of future work is to analyze the statistics, such as entropies, of patterns generated by 1D-ACA to support the hypotheses quantitatively. Another direction is to analyze or develop mechanisms of controlling partial expression and suppression of the properties embedded in the chromosomes, because partial expression is the usual case in biological life.

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Y. Kanada