{
  "id": "2208.08505",
  "version": "v1",
  "published": "2022-08-17T19:52:58.000Z",
  "updated": "2022-08-17T19:52:58.000Z",
  "title": "$Δ$-revolving sequences and self-similar sets in the plane",
  "authors": [
    "Kiko Kawamura",
    "Tobey Mathis"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Initiated by Mizutani and Ito's work in 1987, Kawamura and Allen recently showed that certain self-similar sets generalized by two similar contractions have a natural complex power series representation, which is parametrized by past-dependent revolving sequences. In this paper, we generalize the work of Kawamura and Allen to include a wider collection of self-similar sets. We show that certain self-similar sets consisting of more than two similar contractions also have a natural complex power series representation, which is parametrized by {\\it $\\Delta$-revolving sequences}. This result applies to several other famous self-similar sets such as the Heighway dragon, Twindragon, and Fudgeflake.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-17T19:52:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37B10"
    ],
    "keywords": [
      "self-similar sets",
      "revolving sequences",
      "natural complex power series representation",
      "similar contractions",
      "wider collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}