[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-149237-105":59,"doc-detail-149237-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","lizard-skin-patterns-and-the-ising-model","Lizard Skin Patterns and the Ising Model","","Ocellerated lizard (Timon lepidus) displays a monochromatic black-and-green skin scale pattern whose color-flipping dynamics are modeled by a two-state stochastic cellular automaton. The late-time probability distribution of the pattern matches the canonical probability distribution of the antiferromagnetic Ising model and can arise from dynamics distinct from the commonly used Glauber approach. The study further analyzes Ising-model pattern generation on the triangular lattice in the low-temperature regime and discusses implications for self-organization and selection.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/lizard-skin-patterns-and-the-ising-model/149237/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lizard-skin-patterns-and-the-ising-model/149237.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-17","2026-08-27",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What system is used to model the lizard’s color-flipping dynamics?","Question",{"text":112,"@type":113},"A two-state stochastic cellular automaton describes transitions between black and green states on discretized skin scales.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the Ising model relate to the observed late-time pattern distribution?",{"text":117,"@type":113},"The late-time distribution of patterns produced by the automaton corresponds to the canonical probability distribution of the antiferromagnetic Ising model.",{"name":119,"@type":110,"acceptedAnswer":120},"What distinguishes the dynamics studied from commonly used Glauber dynamics?",{"text":121,"@type":113},"The work shows that the target Ising-like distribution can be generated by dynamics different from the Glauber dynamics adapted for discrete-time settings.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},149237,1787797098,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","Editors' Suggestion Featured in Physics  \nLizard Skin Patterns and the Ising Model  \nSzabolcs Zakany, 1,2 Stanislav Smirnov,3,4,5 and Michel C. Milinkovitch1,2,* 1Department of Genetics and Evolution, University of Geneva, 30 quai Ernest-Ansermet, 1211 Genve, Switzerland  \n2SIB Swiss Institute of Bioinformatics, 1211 Geneva, Switzerland  \n3Section of Mathematics, University of Geneva, 7-9 rue du Conseil-Ge´ne´ral, 1205 Genve, Switzerland  \n4Skolkovo Institute of Science and Technology, 121205 Moscow, Russia  \n5St. Petersburg University, 199034 St Petersburg, Russia  \n (Received 17 May 2021; accepted 16 December 2021; published 27 January 2022)  \nThe ocellated lizard (Timon lepidus) exhibits an intricate skin color pattern made of monochromatic black and green skin scales, whose dynamics of color flipping are known to be well modeled by a stochastic cellular automaton. We show that the late-time probability distribution of the pattern corresponds to the canonical probability distribution of the antiferromagnetic Ising model and can be generated by dynamics different from the commonly-used Glauber. We comment on skin scale patterns generated by the Ising model on the triangular lattice in the low-temperature limit.  \nDOI: 10.1103/PhysRevLett.128.048102  \nIntroduction.—Skin color patterns are highly similar among individuals within a species; i.e., zebras have stripes, but cheetahs have spots. However, the positional details of the pattern change from one individual to the other. Whereas, in many species, individuals exhibit the same pattern all their life, in others they drastically shift between distinct juvenile and adult patterns. A third category involves the progressive transformation of the juvenile pattern into the adult pattern. The ocellated lizard (Timon lepidus) is such a case: The adult dorsal labyrinthine pattern, made of black and green chains of scales [Fig. 1(a)], is generated through a gradual process of greento-black and black-to-green color switching of individual scales. The switching of a single scale typically takes a few weeks and can happen even 3–4 years after the beginning of the process. The resulting pattern is likely to have a classical camouflaging function based on body outline disruption [2–4] .  \nWhile skin colour patterning is classically described by Turing’s reaction-diffusion (RD) equations [5], at the scale of the ocellated lizard’s skin scales these dynamics are effectively described by a two-state stochastic cellular automaton (sCA) [6] with spatial discretization provided by the mesoscopic skin scales and with time steps representing increasing time intervals as the lizard grows. Note that spatial and color-state discretizations both emerge from the superposition of the RD system with the lizard’s skin  \nPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.  \ngeometry [6,7] : Diffusion is reduced at the thin borders of much thicker skin scales such that it homogenizes color within a scale, while color-state transitions occur at sharp scale borders. The flipping probabilities of the sCA [Fig. 1(b)] were inferred in Ref. [6] by monitoring the skin patterns of individuals over a period of several years. Computer simulations of the sCA yield patterns very similar to those of real lizards [6] [g. 1(c)] within the  \ncorresponding number of time steps ( 10–15) . The lizardsCA is an example of an ergodic Markov chain on the space of possible patterns, admitting a stationary probability distribution characterizing the late-time patterns.  \nThe celebrated Ising model [8,9], whose states can be generated dynamically, can be viewed as a simple selforganized pattern production mechanism. It was discovered to describe a wide range of processes in physics (idealized but also real magnetic materials a","cbCainO0ZPEGqSrH","https://ap.wps.com/l/cbCainO0ZPEGqSrH","pdf",940293,"English","# Introduction\n## Pattern formation in ocellated lizard skin\n## Stochastic cellular automaton description\n## Ising model as self-organized pattern mechanism","[{\"question\":\"What system is used to model the lizard’s color-flipping dynamics?\",\"answer\":\"A two-state stochastic cellular automaton describes transitions between black and green states on discretized skin scales.\"},{\"question\":\"How does the Ising model relate to the observed late-time pattern distribution?\",\"answer\":\"The late-time distribution of patterns produced by the automaton corresponds to the canonical probability distribution of the antiferromagnetic Ising model.\"},{\"question\":\"What distinguishes the dynamics studied from commonly used Glauber dynamics?\",\"answer\":\"The work shows that the target Ising-like distribution can be generated by dynamics different from the Glauber dynamics adapted for discrete-time settings.\"}]","Lizard Skin Patterns and the Ising Model | PDF",15]