{"paper":{"title":"Space-filling curves of self-similar sets (I): Iterated function systems with order structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GN","authors_text":"Hui Rao, Shu-Qin Zhang","submitted_at":"2015-09-21T15:37:23Z","abstract_excerpt":"This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets.\n  In the present paper, we introduce a notion of \\emph{linear graph-directed IFS} (linear GIFS in short). We show that to construct a space-filling curve of a self-similar set, it is amount to explore its linear GIFS structures. Some other notions, such as chain condition, path-on-lattice IFS, and visualizations of space-filling curves are also concerned.\n  In sequential papers \\cite{Dai15} and \\cite{RZ14}, we obtain a universal algorithm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06276","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"}