{
  "id": "2108.11382",
  "version": "v1",
  "published": "2021-08-25T16:36:36.000Z",
  "updated": "2021-08-25T16:36:36.000Z",
  "title": "Fractions, Functions and Folding. A Novel Link between Continued Fractions, Mahler Functions and Paper Folding",
  "authors": [
    "Joris Nieuwveld"
  ],
  "comment": "57 pages, 7 figures. Master's Thesis",
  "categories": [
    "math.NT",
    "math.CO",
    "math.CV"
  ],
  "abstract": "Repeatedly folding a strip of paper in half and unfolding it in straight angles produces a fractal: the dragon curve. Shallit, van der Poorten and others showed that the sequence of right and left turns relates to a continued fraction that is also a simple infinite series. We construct a Mahler function from two functions of Dilcher and Stolarsky with similar properties. It produces a predictable irregular continued fraction that admits a regular continued fraction and a shape resembling the dragon curve. Furthermore, we discuss numerous variations on this theme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-25T16:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11B85"
    ],
    "keywords": [
      "continued fraction",
      "mahler function",
      "novel link",
      "paper folding",
      "dragon curve"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}