A Brownian cellular automaton (BCA) is an asynchronous cellular automaton (ACA) in which local configurations representing signals may move forth and back randomly, as if they were undergoing random walks. The random fluctuation offers a natural mechanism to propagate signals in the 2-dimensional cell space, and to cross signals moving in directions perpendicular to each other. As a result, the BCA in (Lee et al., 2016) employs 4 cell states and 17 transition rules to conduct universal computation, both of which are less than other equivalent ACAs in the literature. This paper aims to advance the fluctuation-based scheme one step further, via proposing a new BCA with 4 states and 14 rules that achieves a reduction in the number of transition rules. We show that the BCA is capable of implementing any arbitrary logic circuit, thereby proving its universality in computation. We illustrate this by implementing a circuit that converts a 4-bit number to its equivalent hexadecimal digit.

Numerous varieties of life forms have filled the earth throughout evolution. Evolution consists of two processes: self-replication and interaction with the physical environment and other living things around it. Initiated by von Neumann et al. studies on self-replication in cellular automata have attracted much attention, which aim to explore the logical mechanism underlying the replication of living things. In nature, competition is a common and spontaneous resource to drive self-replications, whereas most cellular-automaton-based models merely focus on some self-protection mechanisms that may deprive the rights of other artificial life (loops) to live. Especially, Huang et al. designed a self-adaptive, self-replicating model using a greedy selection mechanism, which can increase the ability of loops to survive through an occasionally abandoning part of their own structural information, for the sake of adapting to the restricted environment. Though this passive adaptation can improve diversity, it is always limited by the loop’s original structure and is unable to evolve or mutate new genes in a way that is consistent with the adaptive evolution of natural life. Furthermore, it is essential to implement more complex self-adaptive evolutionary mechanisms not at the cost of increasing the complexity of cellular automata. To this end, this article proposes new self-adaptive mechanisms, which can change the information of structural genes and actively adapt to the environment when the arm of a self-replicating loop encounters obstacles, thereby increasing the chance of replication. Meanwhile, our mechanisms can also actively add a proper orientation to the current construction arm for the sake of breaking through the deadlock situation. Our new mechanisms enable active self-adaptations in comparison with the passive mechanism in the work of Huang et al. which is achieved by including a few rules without increasing the number of cell states as compared to the latter. Experiments demonstrate that this active self-adaptability can bring more diversity than the previous mechanism, whereby it may facilitate the emergence of various levels in self-replicating structures.

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