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Full-Text Articles in Dynamical Systems
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Mathematical Sciences Technical Reports (MSTR)
A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and …
New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano
New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano
Rose-Hulman Undergraduate Mathematics Journal
The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences …