{"id":28693188,"url":"https://github.com/ratwolfzero/penrose","last_synced_at":"2025-06-14T08:10:57.038Z","repository":{"id":297261268,"uuid":"996227973","full_name":"ratwolfzero/Penrose","owner":"ratwolfzero","description":"Penrose Tiling Generator","archived":false,"fork":false,"pushed_at":"2025-06-04T17:13:03.000Z","size":10992,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2025-06-04T22:17:04.393Z","etag":null,"topics":["aperiodic-tilings","aperiodicity","golden-ratio","matching-rules","penrose","penrose-lib","penrose-tilings","penrose-triangle","recursive-subdivision"],"latest_commit_sha":null,"homepage":"https://github.com/ratwolfzero/Penrose","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ratwolfzero.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null}},"created_at":"2025-06-04T16:34:34.000Z","updated_at":"2025-06-04T17:13:05.000Z","dependencies_parsed_at":"2025-06-04T22:17:09.077Z","dependency_job_id":"75e2d159-84f9-4e64-93e0-35d0490fe795","html_url":"https://github.com/ratwolfzero/Penrose","commit_stats":null,"previous_names":["ratwolfzero/penrose"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/ratwolfzero/Penrose","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ratwolfzero%2FPenrose","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ratwolfzero%2FPenrose/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ratwolfzero%2FPenrose/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ratwolfzero%2FPenrose/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ratwolfzero","download_url":"https://codeload.github.com/ratwolfzero/Penrose/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ratwolfzero%2FPenrose/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":259783067,"owners_count":22910301,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["aperiodic-tilings","aperiodicity","golden-ratio","matching-rules","penrose","penrose-lib","penrose-tilings","penrose-triangle","recursive-subdivision"],"created_at":"2025-06-14T08:10:54.052Z","updated_at":"2025-06-14T08:10:57.032Z","avatar_url":"https://github.com/ratwolfzero.png","language":"Python","readme":"\n# Penrose Tiling Generator\n\n![Penrose tiling](penrose_tiling.png)\n\n-----\n\n## 📚 Historical Background\n\n**Penrose tilings** are non-periodic tilings discovered by mathematician and physicist **Sir Roger Penrose** in the 1970s. Unlike regular tilings (like square or hexagonal grids), Penrose tilings **never repeat** in a translational sense but exhibit **local fivefold rotational symmetry** and **quasiperiodic order**.\n\nPenrose developed different types of tilings, with **kite and dart** tiling being one of the earliest and most visually iconic forms.\n\nThese tilings became important in **mathematics**, **physics**, and **crystallography** (e.g., explaining structures of quasicrystals), and were also a major influence in **art** (e.g., M.C. Escher's later work).\n\n\u003e 📖 Reference:\n\u003e R. Penrose, \"Pentaplexity: A class of non-periodic tilings of the plane\", *The Mathematical Intelligencer*, 1979.\n\u003e DOI: [10.1007/BF03026814](https://doi.org/10.1007/BF03024384)\n\n-----\n\n## 📐 Triangle-Based Subdivision Tiling\n\nThis version of the program generates Penrose tilings using **iterative subdivision** of **acute (thin)** and **obtuse (thick)** golden triangles based on Penrose’s and Robinson’s substitution rules. It is mathematically equivalent to recursive implementations, but uses an iterative stack-based approach to avoid Python recursion limits.\n\n### Key Characteristics\n\n* **Fixed Initial Pattern:** Uses a symmetrical 10-triangle star (decagonal) as the seed.\n* **Triangle-Based Only:** All tiles are golden triangles — either acute or obtuse.\n* **Iterative Subdivision:** Substitution rules are applied using a controlled iteration stack (avoiding recursion depth errors).\n* **Implicit Matching Rules:** No decorative arcs needed — aperiodicity and matching logic are encoded in the subdivision rules themselves.\n\n\u003e 🔁 **Note:**  \n\u003e While Penrose triangle tilings are defined recursively, this implementation uses a stack to simulate recursion.  \n\u003e This method is widely used in computational geometry and does **not alter the mathematical correctness** of the tiling.\n\n-----\n\n### 🎨 Features\n\n* **Color Modes:**\n  * `mono`: Grayscale mode (all triangles the same).\n  * `type`: Colors based on triangle type (acute or obtuse).\n  * `color`: Colors based on triangle orientation (reveals 5-fold symmetry).\n* **Recursion Depth Control:** Set recursion depth (3–6 recommended).\n* **Export Options:** Save the resulting tiling as `.png` or `.svg`.\n\n### Usage  \n\nUpon running, you’ll be prompted to:  \n\n1. Enter recursion depth (e.g., 4).  \n2. Select a color mode (`mono`/`type`/`color`).  \n3. Optionally save the output (e.g., `tiling.png`). \n\n\n📝 This version offers a cleaner geometric representation and is particularly useful for studying the underlying substitution logic of Penrose tilings without the visual clutter of explicit matching rule enforcement.\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fratwolfzero%2Fpenrose","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fratwolfzero%2Fpenrose","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fratwolfzero%2Fpenrose/lists"}