{"paper":{"title":"Accuracy of the box-counting algorithm for noisy fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"physics.data-an","authors_text":"A. Z. Gorski, J. Skrzat, M. Stroz, P. Oswiecimka","submitted_at":"2014-12-20T15:55:48Z","abstract_excerpt":"The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\\gamma = 10^{-5} \\div 10^{-1}$. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of $\\gamma$ for different sizes of the data sample ($n_{tot}$). In particular, it has been found that a tiny ($10^{-5}$) addition of noise generates much larger (three orders of magnitude) error of the calculated fractal exponents. Natural saturation of the error for larger noise values prohibits the power-li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6664","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"}