Complex Systems
Current Issue

Volume 28, Number 3 (2019)


Lenia: Biology of Artificial Life Download PDF
Bert Wang-Chak Chan

A new system of artificial life called Lenia (from Latin lenis “smooth”), a two-dimensional cellular automaton with continuous spacetime state and generalized local rule, is reported. Computer simulations show that Lenia supports a great diversity of complex autonomous patterns or “life forms” bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation. They differ from other cellular automata patterns in being geometric, metameric, fuzzy, resilient, adaptive and rule generic.

Basic observations of the system are presented regarding the properties of spacetime and basic settings. A broad survey of the life forms is provided and categorized into a hierarchical taxonomy, and their distribution is mapped in the parameter hyperspace. Their morphological structures and behavioral dynamics are described, and possible mechanisms of their self-organization, self-direction and plasticity are proposed. Finally, the study of Lenia and how it would be related to biology, artificial life and artificial intelligence is discussed.

Keywords: artificial life; geometric cellular automata; complex system; interactive evolutionary computation

Cite this publication as:
B. W.-C. Chan, “Lenia: Biology of Artificial Life,” Complex Systems, 28(3), 2019 pp. 251–286.
https://doi.org/10.25088/ComplexSystems.28.3.251


Urbanization, Energy Consumption and Entropy of Metropolises Download PDF
Syed Amaar Ahmad

Metropolises are complex systems comprising social networks, engineering systems, agricultural output, economic activity and energy components. Urbanization stems from both increasing human population levels and expansion in a city’s surface area. In this paper, we develop a model of how the population and area of a city affect its energy consumption patterns. We also show that with urbanization of smaller cities, there is a corresponding increase in the entropy (or variance) of the energy consumption, whereas, for larger cities, the entropy actually diminishes. This result interestingly implies that as metropolises scale, we may have a way to determine the point of a city’s stagnation or decline. In the empirical analysis, we use power-demand data from the island state of Singapore between 2004 and 2019 to illustrate that with population growth, there is a tipping point for variance (or equivalently entropy) in the power demand. Moreover, we also provide a theoretical framework on how population growth and area growth cycles are mutually dependent and expand on how much information can be extracted about the entire city from a subregion. Finally, we show that if the city’s economic size (domestic product etc.) is proportional to the consumed energy, then for a constant population density, the economy scales linearly with the area. Our effort in developing a metropolis growth model is motivated by the need to understand how human behavior and organization at scale affect sustainability and economic growth.

Keywords: complex systems; Pareto-optimality; topological invariance; multi-scalar information; cellular automata; Dyson civilization

Cite this publication as:
S. A. Ahmad, “Urbanization, Energy Consumption and Entropy of Metropolises,” Complex Systems, 28(3), 2019 pp. 287–312.
https://doi.org/10.25088/ComplexSystems.28.3.287


Graph Self-Replication System Download PDF
D Venkata Lakshmi and Jeganathan L

The self-replication introduced by John von Neumann is a process that produces a copy of itself. As a novel approach, this paper studies the self-replication process through the process of reproduction. In this paper, we propose a comprehensive graph reproduction system (GRS) and identify a specific reproduction system that turns out to be a graph self-replication system (GSS), with which a copy of any given graph can be produced through an algorithmic process. Unlike the GRS studied by Richard Southwell, our model considers the evolution of edges along with the evolution of vertices. We analyze some of the existing reproduction models through our system and identify the models that are self-replicable.

Keywords: self-replication; reproduction models; graph reproduction system; graph self-replication system; self-replication of graph; inherent graph self-replication system

Cite this publication as:
D Venkata Lakshmi and Jeganathan L, “Graph Self-Replication System,” Complex Systems, 28(3), 2019 pp. 313–332.
https://doi.org/10.25088/ComplexSystems.28.3.313


Relevance and Importance Preferential Attachment Download PDF
Chjan Lim and Weituo Zhang

Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment (PA) considering these factors. We analyze and compute several important features of the network class generated by this algorithm, including scale-free degree distribution, high clustering coefficient, small-world property and core-periphery structure. We then compare this model with other network models and empirical data such as intercity road transportation and air traffic networks.

Keywords: geometric preferential attachment; network growth; social networks; applied probability; traffic networks

Cite this publication as:
C. Lim and W. Zhang, “Relevance and Importance Preferential Attachment,” Complex Systems, 28(3), 2019 pp. 333–355.
https://doi.org/10.25088/ComplexSystems.28.3.333


Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice Download PDF
Zakarya Zarezadeh and Giovanni Costantini

Memory is a ubiquitous phenomenon in biological systems, in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many phenomena related to memory are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict the extant approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. Along these lines, we can imagine a memory module contributing to cell therapy or the synthetic differentiation of certain cells in a certain fashion after experiencing a brief stimulus. We demonstrate that information processing properties of cellular automata (CAs) can be controlled by a signal composed of excitation pulses. We discuss how cellular memory can be incorporated into more complex systems like CAs to understand the controlling of information processing performed by a medium with the use of a pulse signal propagated from a number of control cells. In this paper, we also investigate the potential application of cellular computation for constructing pseudorandom number generators (PRNGs). Furthermore, the PRNG scheme based on CAs with reaction-diffusion memory is proposed for its capability of generating ultrahigh-quality random numbers. However, the quality bottleneck of a practical PRNG lies in the limited cycle of the generator. To close the gap between the pure randomness generation and the short period, we propose and implement a memory algorithm based on a reaction-diffusion process in a chemical system for Boolean CAs. This scheme is characterized by a tradeoff between, on one hand, the rate of generation of random bits and, on the other hand, the degree of randomness that the series can deliver. These successful applications of the memory modeling framework suggest that this innovative theory is an effective and powerful tool for studying memory processes and conditional chemical reactions in a wide range of complex biological systems. This result also opens a new perspective to apply CAs as a computational engine for the robust generation of pure random numbers, which has important applications in cryptography and other related areas.

Keywords: cellular automata; cryptography

Cite this publication as:
Z. Zarezadeh and G. Costantini, “Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice,” Complex Systems, 28(3), 2019 pp. 357–391.
https://doi.org/10.25088/ComplexSystems.28.3.357

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