Terraforms: Engineering Self-emergent Natural Structures

Terraforms: Engineering Self-emergent Natural Structures | 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 Terraforms: Engineering Self-emergent Natural Structures Matteo Convertino, Enza Migliore, Amedeo Martines This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6166568/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract What is the ultimate determinant of strikingly diverse patterns? Can we find a reflection of empirically fabricated patterns into ecological patterns? Can we use these fabricated patterns to inquire about the ontogeny and optimality of nature’s forms and engineer optimal eco-restoration and environmental applications that leverage materials? In this paper, we propose a simple yet powerful uniform pressure-stress response model where the heterogeneous triphasic mixture’s proportions are the leading control determining networked patterns (Terraforms) from uniform to random topologies with fine-scale hybrid motifs. The clay proportion – as the foundational material bonded by water – is the leading factor determining the topology of the patterns, while the ratio of water and binder (mimicking ecological interactions) is the second-order factor determining patterns’ motifs. Scale-free patterns arise from log-normal materials’ proportions, where the systemic stress and hygroscopy are the minimum and maximum for a universal water/binder ratio equal to the Pacioli golden ratio. Physical sciences/Engineering/Civil engineering Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Earth and environmental sciences/Ecology/Ecological modelling Earth and environmental sciences/Ecology/Ecological networks Terraforms emergence information dimension fractals ecosystemic stress 20 patterns materials‘ proportion Pacioli’s ratio Full Text Additional Declarations No competing interests reported. Supplementary Files SITerraFormsJan25figuressubmitLineNat.pdf Cite Share Download PDF Status: Published Journal Publication published 07 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 23 Apr, 2025 Reviews received at journal 20 Apr, 2025 Reviewers agreed at journal 07 Apr, 2025 Reviews received at journal 05 Apr, 2025 Reviewers agreed at journal 04 Apr, 2025 Reviewers invited by journal 20 Mar, 2025 Editor assigned by journal 20 Mar, 2025 Editor invited by journal 18 Mar, 2025 Submission checks completed at journal 15 Mar, 2025 First submitted to journal 05 Mar, 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. 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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-6166568","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":433834660,"identity":"c6ae3c78-864f-4921-972b-d18c129db339","order_by":0,"name":"Matteo Convertino","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYHADxsYHQJKHj7BKZriWZgOQFjYStDCwSYBJQhp0288f/PBxx2EGg9vNbZVfc+xk2BiYHz66gUeL2ZlkZsmZZ4Ba7hxsuy27LRnoMDZj4xx8Wg4kszHztqUxGNxIbLstuY0ZqIWHTRqvlvOPEVqKJbfVE6HlBtgWG7AWxo/bDhOj5bGx5Mw2Gx7JG4nN0ozbjvOwMRPyy/nEhx8+tknI8d1If/jx57Zqe3725oeP8WmBAR4QwQwhiVAOB4w/SFE9CkbBKBgFIwYAAMOLQ3AH1qiPAAAAAElFTkSuQmCC","orcid":"","institution":"Tsinghua Shenzhen International Graduate School","correspondingAuthor":true,"prefix":"","firstName":"Matteo","middleName":"","lastName":"Convertino","suffix":""},{"id":433834661,"identity":"98c6e761-e9f6-449c-a44d-60523cc7b1aa","order_by":1,"name":"Enza Migliore","email":"","orcid":"","institution":"Southern University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Enza","middleName":"","lastName":"Migliore","suffix":""},{"id":433834663,"identity":"a6777779-0b67-44b5-b5c9-66497baba4fd","order_by":2,"name":"Amedeo Martines","email":"","orcid":"","institution":"Southern University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Amedeo","middleName":"","lastName":"Martines","suffix":""}],"badges":[],"createdAt":"2025-03-06 03:23:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6166568/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6166568/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-18846-6","type":"published","date":"2025-10-07T15:57:25+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93419688,"identity":"d581f3df-566d-46ab-bc4c-0201d5d1aa31","added_by":"auto","created_at":"2025-10-13 16:05:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2058272,"visible":true,"origin":"","legend":"","description":"","filename":"TerraFormsFeb2025submitfigsLineNat.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6166568/v1_covered_6e9c4c54-190a-409e-9f29-3e411e161a25.pdf"},{"id":79539687,"identity":"f7108d34-8e51-48ca-87b0-466fd28ec2a5","added_by":"auto","created_at":"2025-03-31 03:07:43","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":4739073,"visible":true,"origin":"","legend":"","description":"","filename":"SITerraFormsJan25figuressubmitLineNat.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6166568/v1/e40f0b49619f716df1f86c6b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Terraforms: Engineering Self-emergent Natural Structures","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Terraforms, emergence, information dimension, fractals, ecosystemic stress, 20 patterns, materials‘ proportion, Pacioli’s ratio","lastPublishedDoi":"10.21203/rs.3.rs-6166568/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6166568/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"What is the ultimate determinant of strikingly diverse patterns? 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