In this paper, we study stationary patterns of bistable reaction-diffusion cellular automata, i.e., models with discrete time, space and state. We show the rich variability based on the interplay of the capacity and viability and the specific form of reaction functions. While stationary k-periodic patterns occur naturally in many situations in large (exponential) numbers, there exist extreme situations for which there are no heterogeneous patterns. Moreover, nonmonotone dependence of the number of stationary patterns on the diffusion parameter is shown to be natural in the fully discrete setting.

• Klíčová slova
• cellular automata, difference equations, discrete dynamics, patterns, reaction-diffusion,
• MeSH
• biologické modely * MeSH
• celulární automaty * MeSH
• difuze MeSH
• jazyk (prostředek komunikace) MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

Discrete dynamical systems can exhibit complex behavior from the iterative application of straightforward local rules. A famous class of examples comes from cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we relax the regular connectivity grid of cellular automata to a random graph, which gives the class of graph cellular automata. Using the dynamical cavity method and its backtracking version, we show that this relaxation allows us to derive asymptotically exact analytical results on the global dynamics of these systems on sparse random graphs. Concretely, we showcase the results on a specific subclass of graph cellular automata with "conforming nonconformist" update rules, which exhibit dynamics akin to opinion formation. Such rules update a node's state according to the majority within their own neighborhood. In cases where the majority leads only by a small margin over the minority, nodes may exhibit nonconformist behavior. Instead of following the majority, they either maintain their own state, switch it, or follow the minority. For configurations with different initial biases towards one state we identify sharp dynamical phase transitions in terms of the convergence speed and attractor types. From the perspective of opinion dynamics this answers when consensus will emerge and when two opinions coexist almost indefinitely.

• Publikační typ
• časopisecké články MeSH

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Channon, 2006; Ofria & Wilke, 2004; Ray, 1991).

• Klíčová slova
• Classification of complex systems, Turing machines, cellular automata, phase transition, random Boolean networks, transients,
• Publikační typ
• časopisecké články MeSH

Sustainable development goals (SDGs) in the United Nations 2030 Agenda call for action by all nations to promote economic prosperity while protecting the planet. Projection of future land-use change under SDG scenarios is a new attempt to scientifically achieve the SDGs. Herein, we proposed four scenario assumptions based on the SDGs, including the sustainable economy (ECO), sustainable grain (GRA), sustainable environment (ENV), and reference (REF) scenarios. We forecasted land-use change along the Silk Road (resolution: 300 m) and compared the impacts of urban expansion and forest conversion on terrestrial carbon pools. There were significant differences in future land use change and carbon stocks, under the four SDG scenarios, by 2030. In the ENV scenario, the trend of decreasing forest land was mitigated, and forest carbon stocks in China increased by approximately 0.60% compared to 2020. In the GRA scenario, the decreasing rate of cultivated land area has slowed down. Cultivated land area in South and Southeast Asia only shows an increasing trend in the GRA scenario, while it shows a decreasing trend in other SDG scenarios. The ECO scenario showed highest carbon losses associated with increased urban expansion. The study enhances our understanding of how SDGs can contribute to mitigate future environmental degradation via accurate simulations that can be applied on a global scale.

• Klíčová slova
• Carbon pool, Cellular automata, Land-use projection, Scenarios, Sustainable development goals (SDGs), System dynamics model,
• Publikační typ
• časopisecké články MeSH