Samenvatting
In their book Turtle Geometry, Abelson and diSessa formulate and prove the POLY Closing Theorem, which gives an exact condition for when a path produced by the POLY program closes (initial and final turtle position are equal) properly (initial and final turtle heading are equal). The POLY program repeats a translation (Move command) followed by a rotation (Turn command). Their Looping Lemma states that any repeated turtle program is rotation-symmetry equivalent to a POLY program. The POLY Closing Theorem and Looping Lemma are useful in understanding and creating artistic motifs because repeating the same turtle program so that it closes properly, leads to a rotationally symmetric path. In this article, we generalize their result to 3D. A surprising corollary is that when repeating a non-closed non-proper turtle program, its path is closed if and only if it is proper.
Originele taal-2 | Engels |
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Titel | Proceedings of Bridges 2023 |
Subtitel | Mathematics, Art, Music, Architecture, Culture |
Redacteuren | Judy Holdener, Eve Torrence, Chamberlain Fong, Katherine Seaton |
Uitgeverij | Tessellations Publishing |
Pagina's | 425-428 |
Aantal pagina's | 4 |
ISBN van geprinte versie | 978-1-938664-45-8 |
Status | Gepubliceerd - 17 jul. 2023 |
Evenement | 26th Annual Bridges Conference: Mathematics, Art, Music, Architecture, Culture - Dalhousie University, Halifax, Canada Duur: 27 jul. 2023 → 31 jul. 2023 Congresnummer: 26 https://www.bridgesmathart.org/b2023/ |
Publicatie series
Naam | Bridges Conference Proceedings |
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Uitgeverij | Tesselations Publishing |
ISSN van geprinte versie | 1099-6702 |
Congres
Congres | 26th Annual Bridges Conference |
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Verkorte titel | Bridges Halifax 2023 |
Land/Regio | Canada |
Stad | Halifax |
Periode | 27/07/23 → 31/07/23 |
Internet adres |