The Looping Theorem in 2D and 3D Turtle Geometry

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

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-2Engels
TitelProceedings of Bridges 2023
SubtitelMathematics, Art, Music, Architecture, Culture
RedacteurenJudy Holdener, Eve Torrence, Chamberlain Fong, Katherine Seaton
UitgeverijTessellations Publishing
Pagina's425-428
Aantal pagina's4
ISBN van geprinte versie978-1-938664-45-8
StatusGepubliceerd - 17 jul. 2023
Evenement26th Annual Bridges Conference: Mathematics, Art, Music, Architecture, Culture - Dalhousie University, Halifax, Canada
Duur: 27 jul. 202331 jul. 2023
Congresnummer: 26
https://www.bridgesmathart.org/b2023/

Publicatie series

NaamBridges Conference Proceedings
UitgeverijTesselations Publishing
ISSN van geprinte versie1099-6702

Congres

Congres26th Annual Bridges Conference
Verkorte titelBridges Halifax 2023
Land/RegioCanada
StadHalifax
Periode27/07/2331/07/23
Internet adres

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