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nLab > nLab General Discussions: Experiments with vectors and bivectors

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  1. I would like to draw your attention to a curiosity of linear algebra. Simple vector operations create particles in Euclidean space that interact with each other and show different effects. The particles can combine or disintegrate, resonate, and phase lock can be observed. Different initial conditions can lead to very different transient responses.

    The idea of ​​the algorithm is briefly described in [1]. A more detailed description contains [2]. Some pictures of the results are available [3].

    If you want to experiment with vectors yourself, you can download the Java source code "EightPoints01" [4]. This requires the source code of the Java class "StdDraw" by Robert Sedgewick and Kevin Wayne [5].

    By varying the parameters in "EightPoints01" different scenarios can be examined. As examples, some interesting parameter sets are available in [6].

    [1] https://opus4.kobv.de/opus4-ohm/frontdoor/index/index/docId/253
    [2] https://opus4.kobv.de/opus4-ohm/frontdoor/index/index/docId/126
    [3] https://opus4.kobv.de/opus4-ohm/files/34/OhmDoc01.pdf
    [4] https://drive.google.com/file/d/1u3lOz7ydiSstSIm_FsuUGXntsSUUWay/view?usp=sharing
    [5] https://drive.google.com/file/d/1JjF1Z4kmJaEV5BU2P9j0m9IP-BtaosOo/view?usp=sharing
    [6] https://drive.google.com/open?id=1I82uduHWlwbVNCdFygdsM_B6TqtEwKSM

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