Fractal Stability Applied to Forestry Patches

Fractal Stability Applied to Forestry Patches | 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 Research Article Fractal Stability Applied to Forestry Patches Antonio Teófilo Ataide do Nascimento, Stefanie Chaves dos Santos, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2334580/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Context: The fractal analysis has been used by landscape ecologists as a shape metric in order to quantify the complexity of landscape patches. However the use of fractal geometry in ecology possesses an unexplored potential. We then developed a broader study of shapes with unitary fractal dimension. Objectives: Our aim is to amplify the use of fractal dimensions as a metric of shape in the analysis and discovery of forestry landscape patches with unitary fractal dimension. Furthermore, we develop a method for monitoring and recovery of forestry patches. Methods: We establish a method of expansion in order to obtain patches with a good perimeter-area ratio, i. e., unitary fractal dimension. In order to do that, to each landscape patch we associate a polygon and, to each side, we define a locus that expands the polygon so that its fractal dimension is equal to one. Results: This study reveals a range of patches’ shapes with unitary fractal dimension. Inspired by the proposed method's recursion we denote them as fractally stable polygons. To each side of the polygon we set a condition of expansion possibility. The locus of expansion was also defined. Additionally, we define a test of global expansion. Conclusions: Through the developed method it is possible to ascertain when the perimeter-area ratio of a landscape patch is compromised. To expandable sides, the method provides the locus of recovery of the perimeter-area ratio. This enables a wider applicability in the analysis of forestry fragmentation through fractal dimension. Fractal Dimension Landscape Ecology Shape Metrics Forest Patches Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-2334580","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":158655959,"identity":"f737a048-bd3c-4512-bfbb-a6e12fbad1a2","order_by":0,"name":"Antonio Teófilo Ataide do Nascimento","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYPACCQj1AYgNGHgIKGaDa2FmYJxBghYGsBZmHmK08M/vPfjxR41FNL90/8HHtm135MwZeI99wKdF4hhfsjTPMYncmXMOMxvntj0ztmzgS56B15pjPAbSjA0SuRtuJLNJ57YdTtxwgMcYrw75YzzGP38CtewHabFsO1xPUIvBMR4zCV6QLRJALYxthxMMCGkxPJZjZg3yy4wbycaGPecOG+5s5kvGq0Xu8Bnjmz9q6nL7ZyQ+fPCj7LC8OXvvYbxasABmUjWMglEwCkbBKMAAALCLRFWqNe8LAAAAAElFTkSuQmCC","orcid":"","institution":"Universidade do Estado da Bahia","correspondingAuthor":true,"prefix":"","firstName":"Antonio","middleName":"Teófilo Ataide do","lastName":"Nascimento","suffix":""},{"id":158655960,"identity":"4046d90b-b678-4cb8-a7cf-50817d427113","order_by":1,"name":"Stefanie Chaves dos Santos","email":"","orcid":"","institution":"Universidade do Estado da Bahia","correspondingAuthor":false,"prefix":"","firstName":"Stefanie","middleName":"Chaves dos","lastName":"Santos","suffix":""},{"id":158655961,"identity":"9d7ca7b6-9bd0-421d-8ad9-e06953610b19","order_by":2,"name":"Mara Rojane Barros de Matos","email":"","orcid":"","institution":"Universidade do Estado da Bahia","correspondingAuthor":false,"prefix":"","firstName":"Mara","middleName":"Rojane Barros","lastName":"de Matos","suffix":""},{"id":158655963,"identity":"2ea9a8f1-ad3c-4de7-9604-e7bf5ed36b1c","order_by":3,"name":"Maria Dolores Ribeiro Orge","email":"","orcid":"","institution":"Universidade do Estado da Bahia","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"Dolores Ribeiro","lastName":"Orge","suffix":""}],"badges":[],"createdAt":"2022-12-01 16:30:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2334580/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2334580/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":38278438,"identity":"b61db971-16cb-4c32-8082-3d1c97535460","added_by":"auto","created_at":"2023-06-09 10:44:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":837371,"visible":true,"origin":"","legend":"","description":"","filename":"FractalStabilityAppliedtoForestryPatches.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2334580/v1_covered_3a2f3d4c-3dfe-49bf-b4af-b6217cf00439.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fractal Stability Applied to Forestry Patches","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Fractal Dimension, Landscape Ecology, Shape Metrics, Forest Patches","lastPublishedDoi":"10.21203/rs.3.rs-2334580/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2334580/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eContext:\u003c/h2\u003e\u003cp\u003eThe fractal analysis has been used by landscape ecologists as a shape metric in order to quantify the complexity of landscape patches. However the use of fractal geometry in ecology possesses an unexplored potential. We then developed a broader study of shapes with unitary fractal dimension.\u003c/p\u003e\u003ch2\u003eObjectives:\u003c/h2\u003e\u003cp\u003eOur aim is to amplify the use of fractal dimensions as a metric of shape in the analysis and discovery of forestry landscape patches with unitary fractal dimension. Furthermore, we develop a method for monitoring and recovery of forestry patches.\u003c/p\u003e\u003ch2\u003eMethods:\u003c/h2\u003e\u003cp\u003eWe establish a method of expansion in order to obtain patches with a good perimeter-area ratio, i. e., unitary fractal dimension. In order to do that, to each landscape patch we associate a polygon and, to each side, we define a locus that expands the polygon so that its fractal dimension is equal to one.\u003c/p\u003e\u003ch2\u003eResults:\u003c/h2\u003e\u003cp\u003eThis study reveals a range of patches\u0026rsquo; shapes with unitary fractal dimension. Inspired by the proposed method's recursion we denote them as fractally stable polygons. To each side of the polygon we set a condition of expansion possibility. The locus of expansion was also defined. Additionally, we define a test of global expansion.\u003c/p\u003e\u003ch2\u003eConclusions:\u003c/h2\u003e\u003cp\u003eThrough the developed method it is possible to ascertain when the perimeter-area ratio of a landscape patch is compromised. To expandable sides, the method provides the locus of recovery of the perimeter-area ratio. 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