{"paper":{"title":"On geodesics of phyllotaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.NT","authors_text":"Roland Bacher (IF)","submitted_at":"2013-01-31T10:02:51Z","abstract_excerpt":"Seeds of sunflowers are often modelled by the map $n\\longmapsto \\varphi_\\theta(n)=\\sqrt{n}e^{2i\\pi n\\theta}$ leading to a roughly uniform repartition with two consecutive seeds separated by the divergence angle $2\\pi\\theta$ for $\\theta$ the golden ratio. We associate to an arbitrary real divergence angle $2\\pi \\theta$ a geodesic path $\\gamma_\\theta: \\mathbb R_{>0}\\longrightarrow \\mathrm{PSL}_2(\\mathbb Z)\\backslash \\mathbb H$ of the modular curve and use it for local descriptions of the image $\\varphi_\\theta(\\mathbb N)$ of the phyllotactic map $\\varphi_\\theta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7568","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}