Mitered fractal trees: constructions and properties

T. Verhoeff, K. Verhoeff

    Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

    Samenvatting

    Tree-like structures, that is, branching structures without cycles, are attractive for artful expression. Especially interesting are fractal trees, where each subtree is a scaled and possibly otherwise transformed version of the entire tree. Such trees can be rendered in 3D by using beams with a polygonal cross section for the trunk and the branches. The challenge is to connect the beams at the branching points in such a way that the beam edges nicely meet. This is related to the miter joint, but does not necessarily involve ternary miter joints. In this article, we explore a parameterized family of fractal trees that can be rendered with polygonal beams whose edges meet properly at the branching points. We present various constructions and analyze their mathematical properties. Some of these trees have been constructed as artwork in wood and bronze.
    Originele taal-2Engels
    TitelProceedings of Bridges Towson: Mathematics, Music, Art, Architecture, Culture (15th Annual Bridges Conference, Towson MD, USA, July 25-29, 2012)
    RedacteurenR. Bosch, D. McKenna, R. Sarhangi
    UitgeverijTessellations Publishing
    Pagina's25-32
    ISBN van geprinte versie978-1-938664-00-7
    StatusGepubliceerd - 2012
    Evenement15th Annual Bridges Conference (Bridges 2012), July 25-29, 2012, Towson, MD, USA - Towson University, Towson, MD, Verenigde Staten van Amerika
    Duur: 25 jul. 201229 jul. 2012
    http://bridgesmathart.org/past-conferences/bridges-2012/

    Congres

    Congres15th Annual Bridges Conference (Bridges 2012), July 25-29, 2012, Towson, MD, USA
    Verkorte titelBridges 2012
    Land/RegioVerenigde Staten van Amerika
    StadTowson, MD
    Periode25/07/1229/07/12
    Ander2012 Bridges Conference
    Internet adres

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