This paper presents a novel model of artificial biological time series generation. We employed a cellular automata (CA) system that comprises self-replicating and mutually competing loops. Our self-replicating system is an advanced version of Chou & Reggia’s system (Physica D 110, 252–276). The complex self-replicating CA loops were developed using a construction scheme in which we introduce a unique measure of the CA to quantify the activity of the loops. By summing the loop activities globally and observing the time evolution of the sum, we obtain an artificial time series. The power spectrum of the resulting time series exhibits \({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\) scaling behavior. The exponent \(\alpha\) in the \({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\) power spectrum of the unconstrained self-replicating system is \(\alpha \approx 1.5\). Constraints on loop dynamics, leading to larger-scale death in the loop colonies, are implemented in our CA. With the application of the constraints, the value of \(\alpha\) is lowered to nearly 1. The results show that self-replication and death in the CA space play the roles of excitatory and inhibitory synaptic functions, respectively, in a neuronal network. The self-replication/death balance control in our study could modulate the scaling exponent \(\alpha\) in the power spectrum, similar to the activation/inhibition balance control in neural networks and local field potential (LFP) simulations in recent studies. The calculation of the largest Lyapunov exponent, L1, shows the chaotic nature of the time series. The form of our CA system resembles that of neuronal potential transmission and replication to nearby neurons. The results of this study suggest another feasible concept for the origin of biological signals. Executable codes associated with this study are freely accessible.

本文提出了一种新的人工生物时间序列生成模型。我们采用了包含自我复制和相互竞争循环的细胞自动机 (CA) 系统。我们的自我复制系统是 Chou & Reggia 系统 (Physica D 110, 252–276) 的高级版本。复杂的自我复制 CA 循环是使用一种构造方案开发的，在该方案中，我们引入了一种独特的 CA 度量来量化循环的活动。通过对循环活动进行全局求和并观察总和的时间演变，我们获得了一个人工时间序列。由此产生的时间序列的功率谱表现出\({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\)缩放行为。指数\（\阿尔法\）在\({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\)无约束的功率谱自我复制系统是\(\alpha \approx 1.5\)。在我们的 CA 中实施了对循环动力学的限制，导致循环菌落中的大规模死亡。随着约束的应用，\(\alpha\)的值降低到接近1。 结果表明，CA空间中的自我复制和死亡分别在神经元中发挥兴奋性和抑制性突触功能的作用网络。我们研究中的自我复制/死亡平衡控制可以调节缩放指数\(\alpha\)在功率谱中，类似于最近研究中神经网络和局部场电位 (LFP) 模拟中的激活/抑制平衡控制。最大李雅普诺夫指数 L1 的计算显示了时间序列的混沌性质。我们的 CA 系统的形式类似于神经元电位传递和复制到附近神经元的形式。这项研究的结果为生物信号的起源提出了另一个可行的概念。与本研究相关的可执行代码可免费访问。