{"paper":{"title":"Relation between Lacunarity, Correlation dimension and Euclidean dimension of Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.geo-ph"],"primary_cat":"cond-mat.soft","authors_text":"Abhra Giri, Sujata Tarafdar, Tapati Dutta","submitted_at":"2016-02-19T04:25:00Z","abstract_excerpt":"Lacunarity is a measure often used to quantify the lack of translational invariance present in fractals and multifractal systems. The generalised dimensions, specially the first three, are also often used to describe various aspects of mass distribution in such systems. In this work we establish that the graph (\\textit{lacunarity curve}) depicting the variation of lacunarity with scaling size, is non-linear in multifractal systems. We propose a generalised relation between the Euclidean dimension, the Correlation Dimension and the lacunarity of a system that lacks translational invariance, thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06293","kind":"arxiv","version":1},"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"}