Cellular automata | Dynamical systems
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogeneity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolve in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class is thought to be computationally universal, or capable of simulating a Turing machine. Special types of cellular automata are reversible, where only a single configuration leads directly to a subsequent one, and totalistic, in which the future value of individual cells only depends on the total value of a group of neighboring cells. Cellular automata can simulate a variety of real-world systems, including biological and chemical ones. (Wikipedia).
7.1: Cellular Automata - The Nature of Code
This video introduces the concepts and algorithms behind Cellular Automata. (If I reference a link or project and it's not included in this description, please let me know!) Read along: http://natureofcode.com/book/chapter-7-cellular-automata/ http://en.wikipedia.org/wiki/Cellular_autom
From playlist The Nature of Code: Simulating Natural Systems
Cellular Automata are a fantastic demonstration of how a simple set of rules can elicit a complex emergent behaviour. In this video I show John Conway's Game Of Life implemented in quick and simple C++ at the command line. Github: https://github.com/OneLoneCoder/Javidx9/blob/master/Consol
From playlist Interesting Programming
Coding "Conway's Game of Life" Cellular Automaton in C++/ SFML
Coways Game of life is a very famous cellula automaton, created by John Conway. In this video, I implement it in C++ and SFML. ========= DOWNLOAD: https://github.com/Hopson97/CellularAutomaton/releases/tag/v1.1 SOURCE CODE: https://github.com/Hopson97/CellularAutomaton ========= RESOUR
From playlist Creating Cellular Automaton
Coding Wireworld Cellular Automaton in C++/SFML
Hello everybody! This time, I will be creating Wire World, which is little bit different than some of the other cellular automatons i have made, but still quite cool none the less :) Hope you enjoy! ========= DOWNLOAD: https://github.com/Hopson97/CellularAutomaton/releases/ SOURCE CODE:
From playlist Creating Cellular Automaton
Coding "Predator And Prey" Cellular Automaton in C++/ SFML
Thanks "Nimmy" from my discord server for the idea! Wanted to try something a bit different for a change, and here it is: A cellular automaton. ========= DOWNLOAD: https://github.com/Hopson97/CellularAutomaton/releases/ SOURCE CODE: https://github.com/Hopson97/CellularAutomaton =======
From playlist Creating Cellular Automaton
Frank Buss' Hexagonal Cellular Automaton
Frank Buss' Hex Cellular Automaton, initialized with a glider gun and a rake. http://www.frank-buss.de/automaton/hexautomaton.html Generated with Ready: http://code.google.com/p/reaction-diffusion/
From playlist Ready
Cellular Automata Rule-Generating Polynomials
Cellular Automata rules are represented by integers where we encode the output of the function without knowing the details on how it might be implemented. The CellularAutomaton function in Mathematica only requires these integers, along with the values of r and k, to evolve rules for a giv
From playlist Wolfram Technology Conference 2022
The Genetics of Cellular Automata
When John von Neumann proposed cellular automata to investigate artificial life, he modeled the part that defines their behavior as a subsystem. This subsystem is embodied in the cellular automata rules. Researchers have investigated these rules throughout the decades to model not only art
From playlist Wolfram Technology Conference 2021
7.2: Wolfram Elementary Cellular Automata - The Nature of Code
This video covers the basics of Wolfram's elementary 1D cellular automaton. (If I reference a link or project and it's not included in this description, please let me know!) Read along: http://natureofcode.com/book/chapter-7-cellular-automata/#chapter07_section2 A New Kind of Science: h
From playlist The Nature of Code: Simulating Natural Systems
What We've Learned from NKS Chapter 11: The Notion of Computation
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
What We've Learned from NKS Chapter 6: Starting from Randomness
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
The Curtis-Hedlund-Lyndon Theorem | Nathan Dalaklis | math academic talks
This is the second seminar talk that I have given as a math phd student. It is an expository academic talk that I gave as a Math PhD student during my second semester of my second year in my PhD program. The talk concerns the Factors of Symbolic Dynamical Systems and is focused on the Curt
From playlist Academic Talks
What We've Learned from NKS Chapter 3: The World of Simple Programs
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
What We've Learned from NKS Chapter 2: The Crucial Experiment
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Ville Salo: Nilpotent endomorphisms of expansive group actions
We say a pointed dynamical system is asymptotically nilpotent if every point tends to zero. We study group actions whose endomorphism actions are nilrigid, meaning that for all asymptotically nilpotent endomorphisms the convergence to zero is uniform. We show that this happens for a large
From playlist Dynamical Systems and Ordinary Differential Equations
Searching for a 3D Cellular Automaton - Live from the Wolfram Summer School
Stephen goes on a hunt in the computational universe for interesting cellular automata live at the Wolfram Summer School. For upcoming live streams by Stephen Wolfram, please visit: http://www.stephenwolfram.com/livestreams/
From playlist Stephen Wolfram Livestreams
What We've Learned from NKS Chapter 10: Processes of Perception and Analysis
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Coding "Empire" Cellular Automaton in C++/SFML
This is a cellular automaton that I came up with. YouTube compression kinda ruins it, so I highly recommended you watch in highest quality you can, and also download the project to see it for yourself :) Source: https://github.com/Hopson97/Empire Download: https://drive.google.com/open?i
From playlist Creating Cellular Automaton