Mitered fractal trees: constructions and properties

T. Verhoeff, K. Verhoeff

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


    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.
    Original languageEnglish
    Title of host publicationProceedings of Bridges Towson: Mathematics, Music, Art, Architecture, Culture (15th Annual Bridges Conference, Towson MD, USA, July 25-29, 2012)
    EditorsR. Bosch, D. McKenna, R. Sarhangi
    PublisherTessellations Publishing
    ISBN (Print)978-1-938664-00-7
    Publication statusPublished - 2012
    Event15th Annual Bridges Conference (Bridges 2012), July 25-29, 2012, Towson, MD, USA - Towson University, Towson, MD, United States
    Duration: 25 Jul 201229 Jul 2012


    Conference15th Annual Bridges Conference (Bridges 2012), July 25-29, 2012, Towson, MD, USA
    Abbreviated titleBridges 2012
    Country/TerritoryUnited States
    CityTowson, MD
    Other"Mathematics, Music, Art, Architecture, Culture"
    Internet address


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