Search Results (30)

Understanding how complex biological forms emerge and evolve remains a central question in evolutionary and developmental biology. To explore this complexity, we introduce a minimal two-dimensional, cellular automaton (CA)-based model that captures key features of biological development—such as spatial growth, self-organization, and differentiation—while remaining computationally tractable and evolvable. Unlike most abstract genotype–phenotype mapping models, our approach generates emergent morphological complexity through spatially explicit rule-based interactions governed by a simple genetic vector, resulting in self-organized patterns reminiscent of biological morphogenesis. Using simulations, we show that, as observed in empirical studies, the resulting phenotypic distribution is highly skewed: simple forms are common, while complex ones are rare. The model exhibits a strongly non-linear genotype-to-phenotype mapping in such a way that small genetic changes can lead to disproportionately large morphological shifts. Notably, transitions toward complexity are less frequent than regressions to simplicity, reflecting evolutionary asymmetries observed in natural systems. We further demonstrate that, by allowing for mutations in the generative rules, our model is capable of adaptive evolution and even reproducing generic features of tumoral growth. These findings suggest that even minimal developmental rules can give rise to rich, hierarchical patterns and complex evolutionary dynamics, positioning our CA-based model as a powerful tool for investigating how developmental constraints and biases shape morphological evolution. Full article

Additive manufacturing techniques, such as laser-based powder bed fusion of metals (PBF-LB/M), have now gained high industrial and academic interest. Despite its design flexibility and the ability to fabricate intricate components, LPBF has not yet reached its full potential, partly due to the challenges associated with microstructure control. The precise manipulation of the microstructure in LPBF is a formidable yet highly rewarding endeavor, offering the capability to engineer components at a local level. This work introduces an innovative parallelized Cellular Automaton (CA) framework for modeling the evolution of the microstructure during the LPBF process. LPBF involves remelting and subsequent nucleation followed by crystal growth during solidification, which complicates and burdens microstructure simulations. In this research, a novel approach to nucleation seeding and crystal growth is implemented, focusing exclusively on the final stages of melting and solidification, enhancing the computational efficiency by 30%. This approach streamlines the simulation process, making it more efficient and effective. The developed model was employed to simulate the microstructure of an austenitic advanced high-strength steel (AHSS). The model was validated by comparing the simulation results qualitatively and quantitatively with the experimental data obtained under the same process parameters. The predicted microstructure closely aligned with the experimental findings. Simulations were also conducted at varying resolutions of CA cells, enabling a comprehensive study of their impact on microstructure evolution. Furthermore, the computational efficiency was critically evaluated. Full article

Stomata are essential structures in plants for gas exchange, and their opening and closing are influenced by complex external environmental factors. Using Gynura formosana Kitam as the research object, the regulation of stomatal aperture is crucial for ensuring healthy growth. By simulating and predicting the variation in stomatal aperture, it is possible to determine whether the stomatal response is adapted to environmental conditions. Furthermore, predicting environmental factors such as light intensity and electric fields can help adjust stomatal apertures to enhance Gynura formosana Kitam’s adaptability to different conditions. To explore the impact of external factors like light and electric fields on stomatal aperture, this study employs a cellular automaton model, selecting a 24 h period to observe the stomatal variation law. By incorporating the multi-faceted influences of the external environment on the stomatal apertures of both the upper and lower epidermis of Gynura formosana Kitam leaves, a simulation model of stomatal opening and closing based on metacellular automata is proposed. Based on the physiological characteristics and opening and closing laws of stomata, the rule changes of stomatal opening and closing under different environmental conditions were defined, and the stomatal development area was divided into several two-dimensional and three-dimensional cellular spatial structures. The grid of cells in the structure with stomatal “open” and “closed” states was regarded as an intelligent agent. For different environments under the law of change and simulation of the law of change for simulation research, the simulation results and the actual results match, and the law is consistent. In order to ensure the accuracy of the simulation model, 100 training fits were carried out and the results were statistically analyzed, and the average error was kept within 0.05. This model effectively predicts the variations in stomatal apertures on the upper and lower epidermis of Gynura formosana Kitam leaves, providing a theoretical basis for implementing precise control and improving the economic benefits of Gynura formosana Kitam cultivation. Full article

Osteosarcoma is medically defined as a bone-forming tumor with associated bone-degrading activity. There is a lack of knowledge about the network that generates the overproduction of bone. We studied the early stage of osteosarcoma development with mice enduring a periosteum injection of osteosarcoma cells at the proximal third of the tibia. On day 7 (D7), tumor cells activate the over-synthesis of bone-like material inside the medulla. This overproduction of bone is quickly (D13) followed by degradation. Samples were characterized by microfocus small-angle X-ray scattering (SAXS), wide-angle X-ray scattering (WAXS), optical and electron microscopies, and micro-indentation. This intramedullary apatite–collagen composite synthesis highlights an unknown network of bone synthesis stimulation by extramedullary osteosarcoma cells. This synthesis activation mechanism, coupled with the well-known bone induced osteosarcoma growth activation, produces a rare synergy that may enlighten the final osteosarcoma morphology. With this aim, a 3D cellular automaton was developed that only included two rules. Simulations can accurately reproduce the bi-continuous sponge macroscopic structure that was analyzed from mice tumor micro-tomography. This unknown tumor activation pathway of bone synthesis, combined with the known bone activation of tumor growth, generates a positive feedback synergy explaining the unusual sponge-like morphology of this bone cancer. From a biomaterials point of view, how nature controls self-assembly processes remains an open question. Here, we show how the synergy between two biological growth processes is responsible for the complex morphology of a bone tumor. This highlights how hierarchical morphologies, accurately defined from the nanometer to the centimeter scale, can be controlled by positive feedback between the self-assembly of a scaffold and the deposition of solid material. Full article

The fast-paced depletion of fossil fuels and environmental concerns have intensified interest in renewable energies, with dispatchable solar energy emerging as a key alternative. Concentrated solar power (CSP) technology, utilizing thermal energy storage (TES) systems with molten salts at 560 °C, offers significant potential for large-scale energy generation. However, these extreme conditions pose challenges related to material corrosion, which is critical for maintaining the efficiency and lifespan of CSP. This research modeled the corrosion process of 347H stainless steel in molten solar salt (60% NaNO₃ + 40% KNO₃) melted at 400 °C using a cellular automaton (CA) algorithm. The CA model simulated oxide growth under pilot-plant conditions in a lattice of 400 × 400 cells. SEM-EDS imaging compared the model with a mean squared error of 2%, corresponding to a corrosion layer of 4.25 µm after 168 h. The simulation applied von Neumann and Margolus neighborhoods for the ion movement and reaction rules, achieving a cell size of 0.125 µm and 10.08 s per iteration. This study demonstrates the CA model’s effectiveness in replicating corrosion processes, offering a tool to optimize material performance in CSP systems. Additionally, continuing this investigation could contribute to the development of industrial applications, enabling the design of preventive strategies for large-scale operations. Full article

Campylobacter jejuni plays a significant role in human health, food production, and veterinary practice. Biofilm formation is a likely mechanism explaining the survival of C. jejuni in seemingly unfavourable environments, but the underlying mechanisms are poorly understood. We propose a mathematical model to unify various observations regarding C. jejuni biofilm formation. Specifically, we present a cellular automaton with stochastic dynamics that describes both the probability of biofilm initiation and its subsequent growth. Our model incorporates fundamental processes such as cell rearrangement, diffusion of chemical compounds, accumulation of extracellular material, cell growth, lysis, and deactivation due to nutrient scarcity. The model predicts an optimal nutrient concentration that enhances population survival, revealing a trade-off where higher nutrient levels may harm individual cells but benefit the overall population. Our results suggest that the lower biofilm accumulation observed experimentally in aerobic conditions compared to microaerobic conditions may be due to a reduced surface invasion probability of individual cells. However, cells that do manage to invade can generate microcolonies of a similar size under both aerobic and microaerobic conditions. These findings provide new insights into the survival probability and size of C. jejuni biofilms, suggesting potential targets for controlling its biofilm formation in various environments. Full article

Debris flow, driven by natural events like heavy rainfall and snowmelt, involves sediment, rocks, and water, posing destructive threats to life and infrastructure. The accurate prediction of its activity range is crucial for prevention and mitigation efforts. Cellular automata circumvent is the cumbersome process of solving partial differential equations, thereby efficiently simulating complex dynamic systems. Given the anisotropic characteristics of square cells in the simulation of dynamic systems, this paper proposes a novel approach, utilizing a hexagonal cellular automaton for the numerical simulation of debris flows, where the direction judgment efficiency increased by 25%. Employing cubic interpolation, the model thereby determines the central elevation of each hexagonal cell. By modifying the flow direction function and stopping conditions, it achieves more accurate predictions of the debris flow run-out extent. This method was applied to the 2010 Yohutagawa debris flow event and the flume test. To evaluate the simulation’s accuracy, the $\mathsf{\Omega }$ value and $F\beta$ score were used. The $\mathsf{\Omega }$ value is a comprehensive evaluation factor that takes into account missed or misjudgment areas. On this basis, the $F\beta$ score emphasizes that the missed identification of debris flow areas will bring greater harm. Research indicates that the $\mathsf{\Omega }$ value showed improvements of 6.47% and 3.96%, respectively, while the $F\beta$ score improved by 3.10% and 4.61%. Full article

The exploration of the relationship between process parameters and grain evolution during the thermal deformation of rare-earth magnesium alloys using simulation software has significant implications for enhancing research and development efficiency and advancing the large-scale engineering application of high-performance rare-earth magnesium alloys. Through single-pass hot compression experiments, this study obtained high-temperature flow stress curves for rare-earth magnesium alloys, analyzing the variation patterns of these curves and the softening mechanism of the materials. Drawing on physical metallurgical theories, such as the evolution of dislocation density during dynamic recrystallization, recrystallization nucleation, and grain growth, the authors of this paper establish a cellular automaton model to simulate the dynamic recrystallization process by tracking the sole internal variable—the evolution of dislocation density within cells. This model was developed through the secondary development of the DEFORM-3D finite element software. The results indicate that the model established in this study accurately simulates the evolution process of grain growth during heat treatment and the dynamic recrystallization microstructure during the thermal deformation of rare-earth magnesium alloys. The simulated results align well with relevant theories and metallographic experimental results, enabling the simulation of the dynamic recrystallization microstructure and grain size prediction during the deformation process of rare-earth magnesium alloys. Full article

Exploring spatial anisotropy features and capturing spatial interactions during urban change simulation is of great significance to enhance the effectiveness of dynamic urban modeling and improve simulation accuracy. Addressing the inadequacies of current cellular automaton-based urban expansion models in exploring spatial anisotropy features, overlooking spatial interaction forces, and the ineffective expansion of cells due to traditional neighborhood computation methods, this study builds upon the machine learning-based urban expansion model. It introduces a spatial anisotropy index into the comprehensive probability module and incorporates a gravity-guided expansion neighborhood operator into the iterative module. Consequently, the RF-CNN-SAI-CA model is developed. Focusing on the 21 districts of the main urban area in Chongqing, the study conducts comparative analysis and ablation experiments using different models to simulate the land use changes between 2010 and 2020. Different model comparison results show that the recommended model in this study has a Kappa value of 0.8561 and an FOM value of 0.4596. Compared with the RF-CA model and the FA-MLP-CA model, the Kappa values are higher by 0.0407 and 0.1577, respectively, while the FOM values are improved by 0.0529 and 0.0654, respectively. Ablation experiment results indicate that removing gravity, SAI, and expansion neighborhood operators leads to a decrease in both Kappa and FOM values. These findings demonstrate that the RF-CNN-SAI-CA model, based on the expanded neighborhood iteration algorithm, effectively integrates spatial anisotropy features, captures spatial interaction forces, and resolves neighborhood cell failure issues, thereby significantly improving simulation effectiveness. Full article

Although structural topology optimization has been developing for decades, it still plays a leading role within the area of engineering design. Solving contemporary design problems coming from industry requires the implementation of efficient methods and approaches. This stimulates research progress in the development of novel and versatile topology optimization algorithms. To follow these modern trends, an original topology generator has been elaborated and finally built as a Cellular Automaton with original update rules. The motivation for building the algorithm in this way came from the idea of utilizing the benefits of local compliances sorting. This is conducted on two levels: on the global level, the monotonic function mapping local compliances distribution is defined based on their sorted values; on the local level, for each cell, the compliances are sorted within the cell neighborhood. The three largest absolute values are selected, and these are the basis from which to formulate Cellular Automata update rules. These original rules can efficiently control the generation of structural topologies. This technique is somewhat inspired by the grey wolf optimizer strategy, wherein the process of updating design variables refers to the positions of the three best fitted wolves. It is proposed that we refer to the topology algorithm that benefits from the adaptation of sorted compliances optimization as TABASCO. The developed algorithm is a modified version of the flexible Cellular Automata one presented previously. The implemented extension, regarding the local level cell sorting, allows us to improve the resulting compliance values. The advantages of the algorithm, both from numerical and practical engineering points of view, as compared to the others developed within the field, may be gathered as follows: the algorithm works based on simple update rules, i.e., its numerical implementation is not complicated; it does not require gradient computations; filtering techniques are not needed; and it can easily be combined with professional structural analysis programs which allow engineering applications. The developed topology generator has been linked with ANSYS to show that it can be incorporated into a commercial structural analysis package. This is especially important with respect to the engineering implementations. Full article

Bacterial populations often form colonies and structures in biofilm. The paper aims to design suitable algorithms to simulate self-similar evolution in this context, specifically by employing a hybrid model that includes a cellular automaton for the bacterial cells and their dynamics. This is combined with the diffusion of the nutrient (as a random walk), and the consumption of nutrients by biomass. Lastly, bacterial cells divide when reaching high levels. The algorithm computes the space-time distribution of biomass under limited nutrient conditions, taking into account the collective redistribution of nutrients. To achieve better geometry in this modified model approach, truncated octahedron cells are applied to design the lattice of the cellular automaton. This allows us to implement self-similar realistic bacterial biofilm growth due to an increased number of inner relations for each cell. The simulation system was developed using C# on the Unity platform for fast calculation. The software implementation was executed in combination with the procedure of surface roughness measurements based on computations of fractional dimensions. The results of the simulations qualitatively correspond to experimental observations of the population dynamics of biofilm-forming bacteria. Based on in silico experiments, quantitative dependencies of the geometrical complexity of the biofilm structure on the level of consumed nutrients and oxygen were revealed. Our findings suggest that the more complex structure with a fractal dimension of the biofilm boundaries (around 2.6) corresponds to a certain range of nutrient levels, after which the structure degenerates and the biofilm homogenizes, filling the available space provided and tending towards a strictly 3D structure. The developed hybrid approach allows realistic scenario modeling of the spatial evolution of biofilm-forming bacterial populations and specifies geometric characteristics of visualized self-similar biofilm bacterial structures. Full article

Increased use of laser scanning in forest inventories is leading to the adoption and development of automated stand delineation methods. The most common categories of these methods are region merging and region growing. However, recent literature proposes alternative methods that are based on the ideas of cellular automata, self-organizing maps, and combinatorial optimization. The studies where these methods have been described suggest that the new methods are potential options for the automated segmentation of a forest into homogeneous stands. However, no studies are available that compare the new methods to each other and to the traditional region-merging and region-growing algorithms. This study provided a detailed comparison of four methods using LiDAR metrics calculated for grids of 5 m by 5 m raster cells as the data. The tested segmentation methods were region growing (RG), cellular automaton (CA), self-organizing map (SOM), and simulated annealing (SA), which is a heuristic algorithm developed for combinatorial optimization. The case study area was located in the Heilongjiang province of northeast China. The LiDAR data were collected from an unmanned aerial vehicle for three 1500-ha test areas. The proportion of variation in the LiDAR metrics that was explained by the segmentation was mostly the best for the SA method. The RG method produced more heterogeneous segments than the other methods. The CA method resulted in the smallest number of segments and the largest average segment area. The proportion of small segments (smaller than 0.3 ha) was the highest in the RG method while the SA method always produced the fewest small stands. The shapes of the segments were the best (most circular) for the CA and SA methods, but the shape metrics were good for all methods. The results of the study suggest that CA, SOM, and SA may all outperform RG in automated stand delineation. Full article

A nano-scale quantum-dot cellular automaton (QCA) is one of the most promising replacements for CMOS technology. Despite the potential advantages of this technology, QCA circuits are frequently plagued by numerous forms of manufacturing faults (such as a missing cell, extra cell, displacement cell, and rotated cell), making them prone to failure. As a result, in QCA technology, the design of reversible circuits has received much attention. Reversible circuits are resistant to many kinds of faults due to their inherent properties and have the possibility of data reversibility, which is important. Therefore, this research proposes a new reversible gate, followed by a new 3 × 3 reversible gate. The proposed structure does not need rotated cells and only uses one layer, increasing the design’s manufacturability. QCADesigner-E and the Euler method on coherence vector (w/energy) are employed to simulate the proposed structure. The 3 × 3 reversible circuit consists of 21 cells that take up just 0.046 µm². Compared to the existing QCA-based single-layer reversible circuit, the proposed reversible circuit minimizes cell count, area, and delay. Furthermore, the energy consumption is studied, confirming the optimal energy consumption pattern in the proposed circuit. The proposed reversible 3 × 3 circuit dissipates average energy of 1.36 (eV) and overall energy of 1.49 (eV). Finally, the quantum cost for implementing the reversible circuits indicates a lower value than that of all the other examined circuits. Full article

This paper develops the analysis of properties of the cellular automata class introduced by the authors. It is assumed that the set of automaton cells is finite and forms a closed lattice, and there are two states for each automaton cell. We consider a new concept. This concept is the average velocity of a cellular automaton, which characterizes the average intensity of changes in the states of the automaton’s cells for a given initial state. The automaton velocity is equal to 1 if the state of any cell changes at each step. The spectrum of average velocities of a cellular automaton is the set of average velocities for different initial states. Since the state space is finite, the automaton, starting from a certain moment of time, is in periodically repeating states of a cycle, and thus, the research of the velocity spectrum is related to the problem of studying the set of the automaton cycles. For elementary cellular automata, the introduced class consists of a subclass of automata such that the conjugation trasformation of an automaton is the automaton itself (Subclass A) or the reflection of the automaton (Subclass B). For this class, it is proved that the spectrum of the automaton contains the value $v_0$ if and only if the spectrum of the complementary automaton contains the value $1-v_0$ (the sum of the index of elementary cellular automaton and the complementary automaton is 255). For automata of Subclasses A and B, the set of cycles and the velocity spectrum are studied. For Subclass A, a theorem has been proved such that in accordance with this theorem, if two automata complementary to each other start evolving in the same initial state, then the sum of their average velocities is equal to 1. This theorem for Subclass A is generalized to cellular automata, invariant under the conjugation transformation, of more general type than elementary automata. Generalizations of the theorem have been given for the class of one-dimensional cellular automata with a neighborhood containing $2r+1$ cells (the next state of the cell depends on the present states of this cell, r cells on the left and r cells on the right) and for some traditionally considered classes of two-dimensional automata. Some elementary cellular automata belonging to the class considered in the paper can be interpreted as transport models. The properties of the spectra for these automata are studied and compared with the properties of elementary cellular automata not invariant under the considered transformations and can also be interpreted as transport models. The analytical results obtained for these simple models can be used to study the qualitative properties and limiting behavior of more complex transport models. Full article

The efficient modeling of population-density and urban-extent dynamics is a precondition for monitoring urban sprawl and managing the accompanying conflicts. Currently, one of the most promising approaches in this field is cellular automata—spatial models allowing one to anticipate the behavior of unit areas (e.g., evolution or degradation) in response to the influence of their neighborhood. In the present study, the possibility of modeling the population-density and urban-extent dynamics via a cellular automaton with density-specific parameters is tested. Using an adaptive genetic algorithm, three key model parameters (the evolution and degradation thresholds of a cell and its impact upon the neighbors) are optimized to ensure minimal deviation of the model predictions from actual population dynamics data for 24 Ukrainian provinces during three subsequent time windows from 2010–2019. The performance of the obtained optimized models is assessed in terms of the ability to (1) predict population-density classes and (2) discriminate between urban and rural areas. Generally, the obtained optimized models show high performance for both population-density and urban-extent dynamics (with the average Cohen’s Kappa reaching ~0.81 and ~0.91, respectively). Rare cases with poor prediction accuracy usually represent politically and economically unstable Eastern Ukrainian provinces involved in the military conflict since 2014. Statistical analysis of the obtained model parameters reveals significant differences (p < 0.001) in all of them among population-density classes, arguing for the plausibility of the selected density-specific model architecture. Upon exclusion of the above-mentioned Eastern Ukrainian provinces, all model coefficients appear rather stable (p > 0.135) through the three analyzed time windows, indicating the robustness of the model. The ability of the model to discriminate between urban and rural areas depends on the population density threshold. The best correspondence between actual and predicted urban areas emerges upon the 3000 persons/km² population-density threshold. Further improvement of the model seems possible via extending its input beyond the population density data alone, e.g., by accounting for the existing infrastructure and/or natural boundaries—known factors stimulating or inhibiting urban sprawl. Full article