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We investigate the exploration problem of a short-sighted mobile robot moving in an unknown cellular room. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 4 adjacent cells exist and which are boundary…

Computer-aided design for synthetic biology promises to accelerate the rational and robust engineering of biological systems; it requires both detailed and quantitative mathematical and experimental models of the processes to (re)design,…

Architectural design practice has radically evolved over the course of its history, due to technological improvements that gave rise to advanced automated tools for many design tasks. Traditional paper drawings and scale models are now…

We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which one depending on the odometer, and (2) an…

Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is $\Pi^0_2$-complete in dimension 1 and $\Sigma^0_3$-complete in dimension 2 and higher. This…

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the…

We discuss how to construct shift-invariant probability measures over the space of bisequences of symbols, and how to describe such measures in terms of block probabilities. We then define cellular automata as maps in the space of measures…

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules…

This study aims to investigate geometrical concepts related to ethnomathematics in Indonesia. The research design used in this study is to summarize, review, and analyze 24 papers that discussed ethnomathematics. We selected either journal…

Motivated by an application in cell biology, we consider spatial sorting processes defined by particles moving from an initial to a final configuration. We describe an algorithm for constructing a cell complex in space-time, called the…

Based on a group theoretical setting a sort of discrete dynamical system is constructed and applied to a combinatorial dynamical system defined on the set of certain Bethe ansatz related objects known as the rigged configurations. This…

Circuit design based on Quantum-dots Cellular Automata technology offers power-efficiency and nano-size circuits. It is an attractive alternative to CMOS technology. The XOR gate is a widely used building element in arithmetic circuits. An…

In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…

Hierarchical structure is an essential part of complexity, important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple…

Given an algorithm the quality of the output largely depends on a proper specification of the input parameters. A lot of work has been done to analyze tasks related to using a fixed model [25] and finding a good set of inputs. In this paper…