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A continuous automaton can be described as a cellular automaton extended so that the valid states a cell can take are not just discrete (for example,
Continuous_automaton
Discrete model of computation
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called
Cellular_automaton
Study of abstract machines and automata
of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees
Automata_theory
Abstract machines which have a continuum of locations with finite states
A continuous spatial automaton is a type of computer model studied in automata theory, a subfield of computer science. It is similar to a cellular automaton
Continuous_spatial_automaton
Pattern that has no predecessors
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise
Garden of Eden (cellular automaton)
Garden_of_Eden_(cellular_automaton)
Method in computational solid mechanics based on the discrete concept
The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of
Movable_cellular_automaton
with analog physical processes. A hybrid automaton is a finite-state machine with a finite set of continuous variables whose values are described by a
Hybrid_automaton
Type of cellular automaton with similarities to Conway's Game of Life
A cellular automaton (CA) is Life-like (in the sense of being similar to Conway's Game of Life) if it meets the following criteria: The array of cells
Life-like_cellular_automaton
Group whose Cayley graph is an initially subamenable graph
whose state transitions are translation-invariant and continuous) stating that every injective automaton is surjective and therefore also reversible. Ceccherini-Silberstein
Sofic_group
To be the transition function of a cellular automaton, a function from states to states must be a continuous function for this topology, and must also be
Surjunctive_group
the transition function of a one-dimensional cellular automaton if and only if it is continuous (with respect to the Cantor topology) and equivariant
Curtis–Hedlund–Lyndon_theorem
Continuous generalization of cellular automata
intended to be a continuous generalization of Conway's Game of Life, with continuous states, space and time. As a consequence of its continuous, high-resolution
Lenia
Self-reproducing cellular automaton patterns
cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around
Langton's_loops
Deterministic finite automaton accepting set of all suffixes of particular string
In computer science, a suffix automaton is an efficient data structure for representing the substring index of a given string which allows the storage
Suffix_automaton
cyclic cellular automaton is a kind of cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers.
Cyclic_cellular_automaton
Mathematical model for sequential decision making under uncertainty
such an automaton correspond to the states of a "discrete-state discrete-parameter Markov process". At each time step t = 0,1,2,3,..., the automaton reads
Markov_decision_process
Random process independent of past history
steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named
Markov_chain
Cellular automaton that can be run backwards
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells
Reversible_cellular_automaton
Mathematical model of the time dependence of a point in space
the system is called a semi-cascade.[clarification needed] A cellular automaton is a tuple (T, M, Φ), with T a lattice such as the integers or a higher-dimensional
Dynamical_system
Muslim engineer and artist (1136–1206)
robot band designed by al-Jazari. A table device automaton designed by al-Jazari. The hand-washing automaton with a flush mechanism designed by al-Jazari
Ismail_al-Jazari
Dynamical system that exhibits continuous and discrete dynamic behavior
(described by a differential equation) and jump (described by a state machine, automaton, or a difference equation). Often, the term "hybrid dynamical system"
Hybrid_system
Term in distributed computing
most types of an asynchronous concurrent system. On its own, the I/O automaton model contains a very basic structure that enables it to model various
Input/output_automaton
Branch of physics which studies the behavior of materials modeled as continuous media
deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles. Continuum
Continuum_mechanics
Field of computer science
science, a signal automaton is a finite automaton extended with a finite set of real-valued clocks. During a run of a signal automaton, clock values increase
Signal_automaton
Fractal composed of triangles
relating to Conway's Game of Life. For instance, the Life-like cellular automaton B1/S12 when applied to a single cell will generate four approximations
Sierpiński_triangle
Quantum analog of probabilistic automata
)} indicating the probability of the automaton being in an accept state; that is, indicating whether the automaton accepted or rejected the string. The
Quantum_finite_automaton
Book by Stephen Wolfram
discrete rather than continuous. He suggests that space consists of a set of isolated points, like cells in a cellular automaton, and that even time flows
A_New_Kind_of_Science
Book by Konrad Zuse
sort of cellular automaton or other discrete computing machinery, challenging the long-held view that some physical laws are continuous by nature. He focused
Calculating_Space
18th-century automaton or mechanical toy
Tipu's Tiger, Tippu's Tiger or Tipoo’s Tiger is an 18th-century automaton created for Tipu Sultan, the ruler of the Kingdom of Mysore (present day Karnataka)
Tipu's_Tiger
Model to describe distributed systems
finite-state automaton where each transition is labelled by a transition from the Petri net. The Petri net is then synchronised with the finite-state automaton, i
Petri_net
Excitable cellular automaton
The Greenberg–Hastings Cellular Automaton (abbrev. GH model) is a two dimensional cellular automaton (abbrev. CA) named after James M. Greenberg and Stuart
Greenberg–Hastings cellular automaton
Greenberg–Hastings_cellular_automaton
Mathematical proportionality to a square
the input length. The numbers of live cells in space-filling cellular automaton patterns such as the breeder, as a function of the number of time steps
Quadratic_growth
5{\text{m}}/{\text{s}}^{2}} . Although cellular automaton models lack the accuracy of the time-continuous car-following models, they still have the ability
Microscopic traffic flow model
Microscopic_traffic_flow_model
Cellular automaton
to this model as the Abelian sandpile model. The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated
Abelian_sandpile_model
Hungarian and American mathematician and physicist (1903–1957)
kinematic self-reproducing automaton. By 1952, he was treating the problem more abstractly. He designed an elaborate 2D cellular automaton that would automatically
John_von_Neumann
Class of artificial neural network
Guo-Zheng; Giles, C. Lee; Chen, Hsing-Hen (1998). "The Neural Network Pushdown Automaton: Architecture, Dynamics and Training". In Giles, C. Lee; Gori, Marco (eds
Recurrent_neural_network
Form of surveillance in the United States
Critics of the use of technology to track offenders charged it would make "automatons out of our parolees" and in the words of a newspaper editor, "the parole
Electronic monitoring in the United States
Electronic_monitoring_in_the_United_States
recognition engine, specifically a high-performance, two-pass large vocabulary continuous speech recognition (LVCSR) decoder software for speech-related researchers
Julius_(software)
Idea that the universe is a digital computation device
of the universe. The computer could be, for example, a huge cellular automaton. It is deeply connected to the concept of information theory, particularly
Digital_physics
Israeli mathematician and computer scientist (1931–2026)
of Science from Harvard University in 2017. Oblivious transfer Rabin automaton Rabin fingerprint Hyper-encryption List of Israel Prize recipients List
Michael_O._Rabin
Fractal curve
tile the plane. A turtle graphic is the curve that is generated if an automaton is programmed with a sequence. If the Thue–Morse sequence members are
Koch_snowflake
2021 video game
Metroidvania adventure game in which players assume the role of Alma, an automaton who has amnesia in the aftermath of a war between humans and robots. In
Unsighted
Computer built from mechanical components such as levers and gears
for their missiles in the late 80s. In 2016, NASA announced that its Automaton Rover for Extreme Environments program would use a mechanical computer
Mechanical_computer
Topics referred to by the same term
graphs Regular language, a formal language recognizable by a finite state automaton (related to the regular expression) Regular map (graph theory), a symmetric
Regular
Software test automation tool
test cases for one system under test can be modelled using one hybrid automaton. Tests often consist of a sequence of logical phases. The states of the
TPT_(software)
Description of a system using mathematical concepts and language
mathematical models of various machines, an example is the deterministic finite automaton (DFA) which is defined as an abstract mathematical concept, but due to
Mathematical_model
2022 visual novel
"女性配信者育成ADV『NEEDY GIRL OVERDOSE』Steamにて2022年1月21日配信へ。承認欲求の強い女の子との生活で描かれる、さまざまな破滅". Automaton (in Japanese). Active Gaming Media. Archived from the original on November
Needy_Streamer_Overload
English mathematician (1937–2020)
recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the
John_Horton_Conway
2026 video game
from Yoko Taro and Takahisa Taura, leading to last-minute improvements". Automaton. Retrieved 2026-06-14. V, Amber (2026-03-05). "NieR: AAnime-style 3D demon-exorcism
Homura_Hime
Fictional character in a video game
criminals, Alain Guillotin created a clockwork automaton on his sixty-fifth birthday, modeling and naming the automaton after his younger sister, Mary-Ann. He
Sandrone_(Genshin_Impact)
Robot resembling a human
"Androides") to Ephraim Chambers' 1728 Cyclopaedia, in reference to an automaton that St. Albertus Magnus allegedly created. By the late 1700s, "androides"
Android_(robot)
Automaton bird in a decorative box
a box, usually rectangular-shaped, which contains within a miniature automaton singing bird concealed below an oval lid and activated by means of an
Singing_bird_box
2022 survival video game
years, improves multiplayer with in-game voice chat and cross-play]. Automaton Japan (in Japanese). Archived from the original on 11 March 2026. Retrieved
Raft_(video_game)
phenomena in metallic materials, Latest review paper on DRX A Cellular Automaton Model of Dynamic Recrystallization: Introduction & Source Code, Software
Dynamic_recrystallization
Modelling approaches in the field of evacuation simulation: Cellular automaton: discrete, microscopic models, where the pedestrian is represented by
Evacuation_simulation
Instrument for measuring, keeping or indicating time
arrest and release was achieved by gravity exerted periodically as the continuous flow of liquid-filled containers of a limited size. In a single line of
Clock
Use of various control systems for operating equipment
term automation, inspired by the earlier word automatic (coming from automaton), was not widely used before 1947, when Ford established an automation
Automation
Collection of random variables
algorithm Interacting particle system Markov chain Stochastic cellular automaton Random field Randomness Stationary process Statistical model Stochastic
Stochastic_process
Artificial intelligence VTuber
Literature Club!, a posthumanist video game involving AI; Sayoko Narita of Automaton saw the song choice as remorseful and observed that in the return stream
Neuro-sama
Type of stochastic process
doi:10.1214/aop/1176996306. Steif, Jeffrey E. (1994). "The Threshold Voter Automaton at a Critical Point". The Annals of Probability. 22 (3): 1121–1139. doi:10
Interacting_particle_system
2025 video game
Game Awards 2025, two new Silent Hill games announced based on films". Automaton. Harris, Iain (October 3, 2025). "Clair Obscur: Expedition 33 leads the
Silent_Hill_f
Fictional character in a video game
sarcastically touting the worldwide success of Genshin Impact. Ayuo Kawase of AUTOMATON wrote that this dance, originally taken from a meme from Persona 4, represents
Venti_(Genshin_Impact)
1994 science fiction novel by Greg Egan
reality. The Autoverse is an artificial life simulator based on a cellular automaton complex enough to represent the substratum of an artificial chemistry
Permutation_City
2025 video game
"ハイパーインフレパチンコ『Nubby's Number Factory』Steamで「好評率100%」スタート。どことなく2000年代の空気感漂う、奇天烈スコア稼ぎ". AUTOMATON (in Japanese). Archived from the original on 2025-04-03. Retrieved 2025-05-08
Nubby's_Number_Factory
Subfield of computer science and mathematics
the 1960s, states that the entire universe is a huge cellular automaton which continuously updates its rules. Recently it has been suggested that the whole
Theoretical_computer_science
Upcoming video game
mysterious world where you can enjoy everything from adventure to romance.]. Automaton Magazine (in Japanese). Archived from the original on August 25, 2024
Fields_of_Mistria
Game of strategy
the same as three branches of the evolution graph of the Ulam–Warburton automaton. Nim has been mathematically solved for any number of initial heaps and
Nim
Concept in mathematics
transition monoid associated to the semiautomaton of some deterministic finite automaton that recognizes that language. The regular languages over an alphabet
Free_monoid
Structure from which the geometry of the universe arises
the universe acts as an automaton, modifying its structure. Causal set theory is then worked out within this quantum automaton framework to describe a
Pregeometry_(physics)
himself. Mechanical Spiders – A group of automaton spiders created by Hephaestus. Talos – Talos is a giant automaton. Percy, Thalia, and Bianca fight a prototype
List of characters in mythology novels by Rick Riordan
List_of_characters_in_mythology_novels_by_Rick_Riordan
Comic book series
in fact a malformed human living in a life-support tank, using drone automatons to interact with the world. He eventually clones a body from Rex's DNA
Invincible_(comics)
battle between the fierce warrior automatons, Asoka finds the long-lived engineer who had constructed the automatons and is shown how to dismantle and
History_of_robots
2023 turn-based tactical video game
reactivate the device, a defence automaton is activated and identifies the Dolls as intruders, however the automaton is promptly destroyed as Ullrid arrives
Girls'_Frontline_2:_Exilium
Russian mathematician (born 1939)
separate results by the two authors.) Yu. P. Ofman (1965), "A universal automaton". Transactions of the Moscow Mathemathematical Society, volume 14, pages
Yuri_Ofman
Probabilistic cellular automaton Queueing theory Queue Random field Gaussian random field Markov random field Sample-continuous process Stationary process
List of stochastic processes topics
List_of_stochastic_processes_topics
Monstrous Compendium Appendices I & II. Luis Javier Flores Arvizu named the continuous presence of supernatural beings as one of the factors that made Ravenloft
List of Advanced Dungeons & Dragons 2nd edition monsters
List_of_Advanced_Dungeons_&_Dragons_2nd_edition_monsters
Field of mathematics and science based on non-linear systems and initial conditions
to initial conditions. In the discrete-time case, this is true for all continuous maps on metric spaces. In these cases, while it is often the most practically
Chaos_theory
Video game series
Sharp Marker was the most used weapon by top players. Changing trends]. Automaton Media (in Japanese). Archived from the original on 19 January 2025. Retrieved
Splatoon
2016 video game
"Persona 3 Reload's viral "sexy UI" – what ideas went into its design?". AUTOMATON. IGN Staff (December 31, 2021). "The Top 100 Video Games of All Time"
Persona_5
English mathematician (1815–1852)
employed as an "analyst" to provide the workings of a life-sized humanoid automaton. The brass workings of the machine are reminiscent of Babbage's analytical
Ada_Lovelace
Inventor of the telephone (1847–1922)
of the automaton, Bell continued to experiment with a live subject, the family's Skye Terrier, Trouve. After he taught it to growl continuously, Bell would
Alexander_Graham_Bell
Fragment of metric temporal logic
single time unit. Let us now consider a system, such as a timed automaton or a signal automaton, which want to know at each instant whether S holds or not
Metric interval temporal logic
Metric_interval_temporal_logic
the (asymptotical) stability of motion? Is every reversible cellular automaton in three or more dimensions locally reversible? Sudoku: How many puzzles
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Methods that imitate, replicate or use natural processes
the 1960s, states that the entire universe is a huge cellular automaton which continuously updates its rules. Recently it has been suggested that the whole
Natural_computing
Sequence that reads the same forwards and backwards
finite automaton to reliably test for palindromes. In addition, the set of palindromes may not be reliably tested by a deterministic pushdown automaton which
Palindrome
Computational model used in machine learning
Sciences. Rosenblatt F (1957). "The Perceptron—a perceiving and recognizing automaton". Report 85-460-1. Cornell Aeronautical Laboratory. Olazaran M (1996)
Neural network (machine learning)
Neural_network_(machine_learning)
Numerical method for solving physical or engineering problems
of finite element software packages Meshfree methods Movable cellular automaton Multidisciplinary design optimization Multiphysics Patch test Rayleigh–Ritz
Finite_element_method
2025 video game
Academy was actually "two games in one" all along, publisher reveals". Automaton. January 16, 2026. Retrieved April 26, 2026. "The Hundred Line: Last Defense
The Hundred Line: Last Defense Academy
The_Hundred_Line:_Last_Defense_Academy
Museum in West Bloomfield Township, Michigan
which 30 people died, and "Dr. Ralph Bingenpurge", an automaton "food inspector", set up to continuously vomit into a pile of wine bottles, as well as other
Marvin's Marvelous Mechanical Museum
Marvin's_Marvelous_Mechanical_Museum
Application of model-based design
translated to or interpreted as a finite-state automaton or a state transition system. This automaton represents the possible configurations of the system
Model-based_testing
Model of quantum computation
(TM) in the same way that the quantum finite automaton (QFA) generalizes the deterministic finite automaton (DFA). In essence, the internal states of a
Quantum_Turing_machine
Application of mechanics using computational methods
simulation software List of finite element software packages Movable cellular automaton Jamshid Ghaboussi; Xiping Steven Wu (25 November 2016). Numerical Methods
Computational_mechanics
Fictional protagonist of Tomb Raider
"初代『トゥームレイダー』の開発元、日本版の販売担当に「主人公ララ・クロフトの顔をアニメ調に変更して」と求められ断っていた。"日本ウケ"狙いは却下". AUTOMATON. Retrieved 19 January 2026. McFerran, Damien (19 January 2026). "Huge
Lara_Croft
2016 mobile strategy video game
(September 4, 2025). "『ドールズフロントライン（ドルフロ）』Steam版発表。銃火器擬人化キャラの戦いを、ついにPCでプレイ可能に". Automaton (in Japanese). Archived from the original on September 4, 2025. Keiichi
Girls'_Frontline
2013 video game
from Nintendo was this Japanese concept of 'karakuri,' which is these automaton dolls from the 18th century that move as if they were alive. They're actually
Luigi's_Mansion:_Dark_Moon
Symbols for constants, special functions
connection the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine the
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Fictional character in a juvenile mystery series
than the old Nancy because she can be emulated, rather than a "prissy automaton of perfection." (This is more a description of the Nancy of the 1959 revision
Nancy_Drew
Automated software testing technique
input. For instance, LearnLib employs active learning to generate an automaton that represents the behavior of a web application. A white-box fuzzer
Fuzzing
2018 video game
announced that the game reached 250,000 copies sold across all platforms. Automaton reported on June 11, 2024 that the game surpassed 500,000 copies sold
Touhou_Luna_Nights
Matrix used to describe the transitions of a Markov chain
matrix over a continuous state space Matrix difference equation Models of DNA evolution Muirhead's inequality Probabilistic automaton Transition rate
Stochastic_matrix
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON
CONTINUOUS AUTOMATON