Related papers: Formation of morphogenetic patterns in cellular au…
Chemotaxis, i.e. motion generated by chemical gradients, is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular,…
The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a…
Our knowledge of how individual cells self-organize to form complex multicellular systems is being revolutionized by a data outburst, coming from high-throughput experimental breakthroughs such as single-cell RNA sequencing and spatially…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
Models of the dynamics of cellular interaction networks have become increasingly larger in recent years. Formal verification based on model checking provides a powerful technology to keep up with this increase in scale and complexity. The…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Step size in continuous cellular automata (CA) plays an important role in the stability and behavior of self-organizing patterns. Continous CA dynamics are defined by formula very similar to numerical estimation of physics-based ordinary…
The calcium transport in biological systems is modelled as a reaction-diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
Neural Cellular Automata (NCAs) are a model of morphogenesis, capable of growing two-dimensional artificial organisms from a single seed cell. In this paper, we show that NCAs can be trained to respond to signals. Two types of signal are…
In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…
The generation of anisotropic shapes occurs during morphogenesis of almost all organisms. With the recent renewal of the interest in mechanical aspects of morphogenesis, it has become clear that mechanics contributes to anisotropic forms in…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process…
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…