The Smooth Power of the 'Neandertal Method'

The Smooth Power of the 'Neandertal Method' | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article The Smooth Power of the 'Neandertal Method' Aaron Montag, Tim Reinhardt, Jürgen Richter-Gebert This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7217680/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Mar, 2026 Read the published version in The Mathematical Intelligencer → Version 1 posted 7 You are reading this latest preprint version Abstract We describe an algorithmic method to transform a Euclidean wallpaper pattern into a \emph{Circle Limit}-style picture à la Escher. The design goals for the method are to be mathematically sound, aesthetically pleasing and fast to compute. It turns out that a certain class of conformal maps is particularly well-suited for the problem. Moreover, in our specific application, a very simple method – sometimes jokingly called the ''Neandertal method'' for its almost brutal simplicity – proves to be highly efficient, as it can easily be parallelized to be run on the GPU, unlike many other approaches. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Mar, 2026 Read the published version in The Mathematical Intelligencer → Version 1 posted Editorial decision: Revision requested 25 Oct, 2025 Reviews received at journal 24 Oct, 2025 Reviewers agreed at journal 13 Oct, 2025 Reviewers invited by journal 13 Oct, 2025 Editor assigned by journal 07 Aug, 2025 Submission checks completed at journal 07 Aug, 2025 First submitted to journal 25 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7217680","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":534320546,"identity":"7db1b272-6f13-471d-a50f-fd3234ec2290","order_by":0,"name":"Aaron Montag","email":"","orcid":"","institution":"Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Aaron","middleName":"","lastName":"Montag","suffix":""},{"id":534320547,"identity":"801b04d2-277f-4df2-9511-0ec712f76473","order_by":1,"name":"Tim Reinhardt","email":"","orcid":"","institution":"Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Tim","middleName":"","lastName":"Reinhardt","suffix":""},{"id":534320548,"identity":"a442371f-0087-4d1c-9713-6c805dcf5637","order_by":2,"name":"Jürgen Richter-Gebert","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAo0lEQVRIiWNgGAWjYDACZgY2ECUH5vAQreUAA4MxD/FaGCBaEnuI1mLezvzs8YeKe+n7JbITGN5UEKFF5jCbucGBM8W5PRK5GxjnnCFCiwQzD5vEwbYEsBZm3jaitfxLSOcBa/lHtJaGhASIlgaitLCZSZw5lmDYc+bthoNzjhGjhf/wM4mKmgR59vbcjQ/e1BChBQUcIFXDKBgFo2AUjAIcAAB5zS/A9xTi4AAAAABJRU5ErkJggg==","orcid":"","institution":"Technical University of Munich","correspondingAuthor":true,"prefix":"","firstName":"Jürgen","middleName":"","lastName":"Richter-Gebert","suffix":""}],"badges":[],"createdAt":"2025-07-26 00:38:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7217680/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7217680/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00283-025-10492-0","type":"published","date":"2026-03-05T15:57:48+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94456521,"identity":"7b11626d-8cf6-4791-9c80-aaf35166d0dc","added_by":"auto","created_at":"2025-10-27 14:44:38","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4736,"visible":true,"origin":"","legend":"","description":"","filename":"fa338c4a8e2a4a7497d61868857a81bf.json","url":"https://assets-eu.researchsquare.com/files/rs-7217680/v1/ac66229796f01aeaec4fab86.json"},{"id":104251450,"identity":"a31fd3bd-df8d-4af6-a019-b9ea83ec740f","added_by":"auto","created_at":"2026-03-09 16:13:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12906940,"visible":true,"origin":"","legend":"","description":"","filename":"Neandertal20250808.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7217680/v1_covered_43527343-92f8-4387-9303-d627fa88663d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Smooth Power of the 'Neandertal Method'","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-mathematical-intelligencer","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tmin","sideBox":"Learn more about [The Mathematical Intelligencer](http://link.springer.com/journal/283)","snPcode":"283","submissionUrl":"https://submission.nature.com/new-submission/283/3","title":"The Mathematical Intelligencer","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7217680/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7217680/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We describe an algorithmic method to transform a Euclidean wallpaper pattern into a \\emph{Circle Limit}-style picture à la Escher. 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