Cellular_automaton - Wikiparency

# Cellular automaton A cellular automaton is a discrete lattice of cells whose states evolve synchronously according to local neighborhood rules. Simple deterministic or probabilistic update functions generate complex global patterns, Turing-universal computation ([[Conway's_Game_of_Life|Game of Life]], Rule 110), and models of physical, biological, and computational processes.  ## Microsims (promoted from legacy — three.js first) ### MicroSim spec - **Recommended sim type:** cellular automaton - **Microsimmability score:** 94/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Rule number` - `Initial density` - `Steps` ### What animates Each row of cells updates from its neighbors, growing nested or chaotic patterns as the rule changes. ### Learning objective Show how a one-line rule produces complex global patterns. ### MicroSim spec - **Recommended sim type:** cellular automaton - **Microsimmability score:** 95/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Rule number` - `Density` - `Grid size` ### What animates A grid of cells updates each step according to a local rule, growing patterns from a seed row. ### Learning objective Show how simple local rules on a cell grid generate complex global patterns.   ## Images <figure class="wt-gifplate"> <img src="https://commons.wikimedia.org/wiki/Special:FilePath/Conways_game_of_life_breeder_animation.gif" alt="Self-Replication" loading="lazy" decoding="async"> <figcaption><strong>Self-Replication</strong> — Watch self-replicating patterns grow from simple rules.<br> <span class="wt-credit">Wikimedia Commons · <strong>licence pending verification</strong> (run <code>g17_gif_verify.py</code> on a networked lane) · <a href="https://commons.wikimedia.org/wiki/File:Conways_game_of_life_breeder_animation.gif">Details</a></span></figcaption> </figure> *This page has no interactive build yet, so the plate carries the concept. It is the first thing that moves on [[Cellular_automaton]].*  ## Reveal %%REVEAL:p5%% %%REVEAL:svg%% --- *Concept aligned with [Wikipedia](https://en.wikipedia.org/wiki/Cellular_automaton); adapted text, where present, is licensed [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/).* ## Overview [[John_von_Neumann|John von Neumann]] and [[Stanisław_Ulam|Stanisław Ulam]] invented the lattice world to study [[Self-replication|self-replication]]; [[John_Horton_Conway|John Horton Conway]]'s Game of Life made it famous, [[Stephen_Wolfram|Stephen Wolfram]]'s [[A_New_Kind_of_Science|A New Kind of Science]] classified its rule space, and [[Langton's_ant|Langton's ant]] walks the [[Edge_of_chaos|edge of chaos]] where computation lives. Formally it sits inside [[Automata_theory|automata theory]] as a discrete [[Model_of_computation|model of computation]] descended from [[Alan_Turing|Turing]]. As a modeling instrument it discretizes [[Statistical_mechanics|statistical mechanics]] and [[Thermodynamics|thermodynamics]], mimics the [[Reaction–diffusion_system|reaction–diffusion system]] and [[Phase_transition|phase transitions]], generates [[Patterns_in_nature|patterns in nature]] for [[Mathematical_and_theoretical_biology|mathematical biology]] and [[Artificial_life|artificial life]], seeds [[Cryptography|cryptographic]] and [[Pseudorandom_number_generator|pseudorandom]] machinery, and pairs with the [[Agent-based_model|agent-based model]] as the grid-world half of executable [[Physics|physics]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Cellular_automaton) : [Wikitube](https://en.wikitube.io/wiki/Cellular_automaton) ## Previous hub tags Hubs: `Systems`. Portals: [[PORTAL_Systems]], [[PORTAL_Cellular_automaton]].  ## Microsims — three.js (Wolfram classification) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Wolfram_classes_landscape_3D.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Wolfram classes landscape — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy — the fifth of [[PORTAL_Cellular_automaton]]'s five hand-built three.js stations, wired here on the hub article since Wolfram's classification is a section of the Cellular automaton topic rather than a separate Wikipedia article of its own.</p> Stephen Wolfram proposed sorting cellular automaton behaviour into four qualitative classes: Class I (homogeneous, dies to a uniform state), Class II (periodic or nested, simple stable structures), Class III (chaotic, statistically random-looking), and Class IV (complex, localized glider-like structures that interact intricately — rule 110 was proved Turing-complete by Matthew Cook in 2004, and rule 54 is conjectured capable of the same). This build runs four elementary rules side by side as parallel growing 3D terrain strips, one per class, reusing the rule-table/step-row logic of the [[Elementary_cellular_automaton|elementary cellular automaton]] microsim, with a toggle to swap the Class IV strip between rule 110 and rule 54 and a live HUD readout of which rule is running in each strip. --- *Repopulated 2026-08-05 · existing three.js asset wired to the hub · 0 deletions.*