Hybrid Cellular Automata for Manipulating Complex and Chaotic Cellular Automata

Cellular Automata (CA) are powerful simulation tools that operate through discrete elements and associations. CA undirected neighborhood searches may produce specific grain shapes (e.g., octahedral, cuboctahedral, cubic), but not spherical ones. However, in recrystallization modeling, the spherical shape plays a crucial role. Thus, Hybrid Cellular Automata (HCA) share several properties with CA but operate in both continuous and discrete modes simultaneously. Unlike deterministic CA, HCA enable equiaxial grain growth without the need for additional correction algorithms, generating grains that remain initially spherical until they encounter boundaries. This behavior has been addressed by other simulation techniques, but HCA provide a simple and highly effective alternative. In this work, HCA are described in detail, including their foundational principles, algorithm performance, calibration, and potential results. The findings highlight the capability of HCA for straightforward and accurate recrystallization simulations with equiaxial growth.

A novel image encryption algorithm based on a hybrid model of deoxyribonucleic acid (DNA), cellular automata (CA) and chaotic system is proposed. CA due to its complex behavior has several applications such as generating random numbers and cryptography. DNA rules, DNA sequence XOR operator and CA rules are used simultaneously to encrypt the plain-image pixels. To determine rule number in DNA sequence and also CA, a 2-dimension logistic map is employed. Experimental results show that the proposed image encryption scheme has a lot of characteristics, including large key space, low correlation of adjacent cipher pixels, and high security, which can effectively protect the security of the encrypted image.

This paper presents a new methodology for obtaining optimal topologies in continuum structures for compliant mechanism design. This non-gradient approach uses the Hybrid Cellular Automaton (HCA) method. The HCA method is a biologically inspired algorithm that has been used for structural topology optimization. HCA divides the design domain into a lattice of cellular automata (CAs). Locally, each CA is able to modify a continuum structural design variable based on the energy in its neighborhood. A global structural analysis using a flnite element method is used to obtain the information for each iteration. The local change in the design variable is determined by a local design rule. In previous applications to structural optimization, these local rules were implemented to achieve uniform strain energy density throughout the structural when loaded. In the application to compliant mechanisms, the structure must exhibit both ∞exibility and rigidity are required. The mechanism must be able to transfer a force from an input location to the output location while being able to withstand the input force. Therefore a multi-objective formulation is considered so that a uniform distribution of a combination of the two objectives is achieved. The algorithm has shown to be e‐cient as well as resulting in topologies that distribute compliance in uniform manner in that hinges are avoided. In this paper, we will illustrate the use of HCA in 2D and 3D compliant mechanism design using a static nonlinear analysis allowing for large deformations.

The hybrid cellular automaton (HCA) method has been successfully applied to nonlinear transient topology sizing optimization for crashworthiness design. This method utilizes the cellular automata (CA) computing paradigm and nonlinear transient nite element analyses (FEA). In earlier eorts, the HCA algorithm has been used to develop an ecien t methodology for synthesizing sheet metal structures with optimal material thickness distribution under a dynamic loading event using a thickness based topology sizing optimization. In thickness based topology optimization, the objective is to redistribute element thickness to meet the desired performance constraints. The objective in crashworthiness design is to generate energy absorbing structures which can be obtained by uniformly distributing internal energy density (IED). In this paper, the HCA algorithm is utilized to do simultaneous thickness and cost optimization for structures suitable to be manufactured by the tailor welded blank (TWB) technology for signican t mass savings. The sheet metal structure can have dieren t material parts, and the optimum distribution of the material and thickness is obtained to meet the desired performance using nonlinear transient analysis. This methodology is used to tackle complicated problems that involve dynamic events, such as impacts and collisions. The existing commercial thickness optimization tools utilize models under static loading conditions because of the complexities associated with dynamic/impact loading and they are not suitable for design with multiple material and thickness distribution simultaneously. The HCA based thickness optimization algorithm employs nonlinear transient analysis (via LS-Dyna) to capture material and geometric nonlinearities that occur during a dynamic crash event. Therefore by applying this method to impact problems, the resulting structure will account for all phenomena involved. The eectiv eness of the algorithm is demonstrated using a at plate and C-section rail example problem subjected to single or multiple dynamic impact loading. The structures synthesized by the HCA algorithm are able to meet the manufacturing as well as performance constraints.

The hybrid cellular automaton (HCA) method has been successfully applied to nonlinear transient topology optimization for crashworthiness design. This method utilizes the cellular automata (CA) computing paradigm and nonlinear transient nite element analyses (FEA). The objective in crashworthiness design is to generate energy absorbing structures which can be obtained by uniformly distributing internal energy density (IED). In this paper, the HCA algorithm has been utilized to develop an ecien t methodology for synthesizing shell-based structures with optimal material thickness distribution under a dynamic loading event using a thickness based topology optimization. The objective of traditional topology optimization is to redistribute the material within a specied design domain in order to maximize some desired mechanical performance under specied constraints. In thickness based topology optimization, the objective is to redistribute element thickness to meet the desired performance constraints. This methodology is used to tackle complicated problems that involve dynamic events, such as impacts and collisions. The existing commercial thickness optimization tools utilize models under static loading conditions because of the complexities associated with dynamic/impact loading. The HCA based thickness optimization algorithm employs nonlinear transient analyses (via LS-Dyna) to capture material and geometric nonlinearities that occur during a dynamic crash event. Therefore by applying this method to impact problems, the resulting structure will account for all phenomena involved. The eectiv eness of the algorithm is demonstrated using a at plate and C-section rail example problem subjected to dynamic impact loading. The structures synthesized by the HCA algorithm are able to meet the manufacturing as well as performance constraints.

The VLSI implementation of mod-p multipliers, where p is prime, using homomorphisms and one-dimensional hybrid cellular automata (HCA) is presented. This new technique uses the maximum-length cycle produced by HCA, to realise implementation using the minimum possible number of cells in the array. A new theorem on homomorphisms shows how a cyclic group can be mapped into a state group of HCA, of smaller order, which can be implemented more simply than the original. The technique is demonstrated through the VLSI implementation of a modest, mod-127 multiplier. Significant reductions in silicon area, about 95%, are achieved relative to a previous approach that used two-dimensional cellular automata (CA). Layout of the mod-127 multiplier chip has been realised using dual-layer metal, 1.5 μm, n-well, CMOS technology from European Silicon Structures (ES2). Total silicon area is 1.2×0.8 mm2 comprising about 2100 transistors, and multiplication can be obtained up to a maximum clock frequency of 66 MHz. This approach is shown to be encouraging for implementing large devices in terms of silicon area but performance is disappointing. The work demonstrates the flexibility of the HCA array architecture, in terms of modularity, parallelism and local communications; it is particularly well suited for VLSI implementations.

In this paper, we study the characterization of uniform cellular automata with the restricted vertical neighborhood and hybrid cellular automata with both restricted vertical neighborhood and Von Neumann Neighborhood using reflecting boundary condition over the eld ℤ2. The transition rule matrix for uniform and hybrid cellular automata with reflecting boundary condition is obtained and also reversibility of the uniform cellular automata is studied.

Cellular automaton (CA) models have been used to simulate biological phenomena for over sixty years. In previous research, CA principles were applied to solve topology optimization problems using the hybrid cellular automaton (HCA) method. This method combines local evolutionary design rules with finite element analysis. Different control strategies, incorporated into the design rules, seek to minimize the error between a local mechanical signal and its optimum value. The HCA algorithm has demonstrated to be an efficient computational technique since optimal (black and white) topologies are obtained after a few iterations without checker-board patterns [4]. With a change in the objective function, the HCA method was also applied to compliant mechanisms design in a continuum design domain [3]. Nonlinear finite element analysis was incorporated into the algorithm [2]. Typically, a mass constraint is required to obtain slender flexible structures [1]. This constraint is satisfied by calculating the exact value of the associated Lagrange multiplier in every iteration. The objective of this work is to develop a new mass control strategy. In the proposed approach, the value of the Lagrange multiplier is corrected gradually during the iterative process and its final value is found at convergence. This strategy is implemented in both two- and three-dimensional models. The results are compared with the ones obtained using other approaches.

In this paper a FPGA implementation of a cellular automaton defined by rule 101 and it's negate is presented. Such HCA (hybrid cellular automata) was previously proved to behave as a pseudo noise sequence generator with the additional binary synchronization property and with demonstrated capabilities in reducing the overall complexity of image transmission systems. The raster scan is replaced by a chaotic scan provided by HCA. That allows implementation a progressive image compression and spread spectrum transmission with the advantage in low complexity implementation. A VHDL description of the HCA counter is provided for an arbitrary number of cells n. The resulting hardware complexity is several tens of times lower than needed for implementation of other pseudo noise generators reported in the literature.

Foam shock-absorbing structures such as cushioned packages are often utilized to protect various products from mechanical shock and vibration during transportation. The goal of packaging design engineers is to design a cushioned package structure that improves the shock-absorbing performance and minimizes the volume of the package. Some optimization techniques, combined with computational simulation, provide engineers with a way to design an optimal structure. In this paper, we propose a modified topology optimization method suitable for a polymeric foam shock-absorbing structure under dynamic drop loads in multiple directions. Our approach uses a heuristic topology optimization method, known as the Hybrid Cellular Automata (HCA). The HCA algorithm uniformly distributes internal energy density and controls the relative density of Cellular Automata (CAs) making up the design space. This allows the algorithm to maintain or increase the performance of shock absorption and to decrease the amount of material. In particular, this paper presents a modified Solid IsotropicMaterial with Penalization (SIMP) model for foam materials, which parameterizes the design region and interpolates the material properties. We attempt to optimize a simple bottom-cushioned package for a refrigerator by using the proposed foam SIMP model with commercial software: LS-DYNA for drop dynamic simulation and LS-OPT/Topology for the HCA algorithm. Drop simulation and topology optimization are performed considering multiple drop-directions. As a result, our method removes elements that are not related to the shock-absorption performance and provide an optimal cushioning structure using foam material.

Each year, bone metabolic diseases affect millions of people of all ages, genders, and races. Common diseases such as osteopenia and osteoporosis result from the disruption of the bone remodeling process and can place an individual at a serious fracture risk. Bone remodeling is the complex process by which old bone is replaced with new tissue. This process occurs continuously in the body and is carried out by bone cells that are regulated by numerous metabolic and mechanical factors. The remodeling process provides for various functions such as adaptation to mechanical loading, damage repair, and mineral homeostasis. An improved understanding of this process is necessary to identify patients at risk of bone disease and to assess appropriate treatment protocols. High-fidelity computer models are needed to understand the complex interaction of all parameters involved in bone remodeling. The primary focus of this investigation is to present a new computational framework that utilizes mathematical rules to mechanistically model the cellular mechanisms involved in the bone remodeling process. The computational framework used in this research combines accepted biological principles, cellular-level rules in a cellular automaton framework, and finite-element analysis. This computational model is referred to as hybrid cellular automaton (HCA) model. The simulations obtained with the HCA model allow to predict time-dependent morphology variations at the tissue level as a result of biological changes at the cellular level.

This paper exploits an interesting property of a certain type of elementary cellular automata, namely hybrid cellular automata (HCA) defined by rule 101 and its negate. Such HCA may be easily implemented on any CNN platform, and has some interesting properties. It provides a chaotic counting automaton instead of the traditional raster scan counter addressing the multiple sensing elements. Replacing raster scan with chaotic scan provided by the HCA allows implementation of both progressive image compression and spread spectrum transmission with a very low complexity of the transmitting sensor. The clear advantages of our system in terms of implementation complexity, makes it a valuable candidate for low power sensor networks applications.

The concept of hybrid in space‐time Cellular Automata is introduced, for the first time, in this paper, and it is suggested that non‐linear hybrid in space‐time Cellular Automata can be used as pseudorandom pattern generators for VLSI systems, because they can produce patterns with various densities of “1”, distributed at will in space and time. The cycle lengths of non‐linear hybrid Cellular Automata can be estimated using Lyapunov exponents.

Long-range correlations in chaotic cellular automata

Design for structural topology optimization is a method of distributing material within a design domain of prescribed dimensions. This domain is discretized into a large number of elements in which the optimization algorithm removes, adds, or maintains the amount of material. The resulting structure maximizes a prescribed mechanical performance while satisfying functional and geometric constraints. Among di erent topology optimization algorithms, the hybrid cellular automaton (HCA) method has proven to be efcient and robust in problems involving large, plastic deformations. The HCA method has been used to design energy absorbing structures subject to crash impact. The goal of this investigation is to extend the use of the HCA algorithm to the design of advanced armor systems subject to a blast load. The proposed algorithm drives the optimal distribution of a metallic phase and void, or two metallic phases, within the design domain. When the blast pressure wave hits the targeted structure, the uids kinetic energy is transformed into internal energy (IE) inside the solid medium. Maximum attenuation is reached when IE is maximized. Along with an optimum use of material, this condition is satised when IE is uniformly distributed in the design domain. This work makes use of the CONWEP model developed by the Army Research Laboratory and the DRDC plate model developed at Valcartier. The resulting structures show the potential of the HCA method when designing blast mitigating armor structures.