{"paper":{"title":"A construction of fractal surfaces with function scaling factors on a rectangular grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chol-Hui Yun, Hui-Chol Choi, Hyong-Chol O","submitted_at":"2014-04-03T10:49:12Z","abstract_excerpt":"A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1300","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"}