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A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
Simulations of SiC crystal growth using molecular dynamics (MD) have become popular in recent years. They, however, simulate very fast deposition rates, to reduce computational costs. Therefore, they are more akin to surface sputtering,…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
The advantage of Cellular Potts Model (CPM) is due to its ability for introducing cell-cell interaction based on the well known statistical model i.e. the Potts model. On the other hand, Lattice gas Cellular Automata (LGCA) can simulate…
Developmental Graph Cellular Automata (DGCA) are a novel model for morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we show that DGCAs can be trained to grow reservoirs. Reservoirs are grown with two…
Crystallization processes at the mesoscopic scale, where faceted, dendritic growth, and multigrain formation can be observed, are of particular interest within materials science and metallurgy. These processes are highly nonlinear,…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Cellular automata (CA), originally developed as computational models of natural processes, have become a central subject in the study of complex systems and generative visual forms. Among them, the Ulam-Warburton Cellular Automaton (UWCA)…
The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
This paper proposes a new pattern of two dimensional cellular automata linear rules that are used for efficient edge detection of an image. Since cellular automata is inherently parallel in nature, it has produced desired output within a…
Diffusion models have enabled remarkably high-quality medical image generation, yet it is challenging to enforce anatomical constraints in generated images. To this end, we propose a diffusion model-based method that supports…
We use hierarchical procedural rules for the generation of control maps within the stable diffusion framework to produce photo-realistic architectural facade images. Starting from a single input image and its segmentation, we apply an…
We present a new method for simulating crystal growth by energetic beam deposition. The method combines a Kinetic Monte-Carlo simulation for the thermal surface diffusion with a small scale molecular dynamics simulation of every single…