Visualizing Card Shuffling and Permutations in 3D

  September 30, 2020

I have previously worked on visualizations of card shuffling and permutations, and I wanted to extend this to 3D. This is one attempt to do so. This 3D printed object illustrates two perfect out-shuffles with thirty-six cards and six piles. Each curve, from top to bottom, represents a single card, and after two perfect out-shuffles, the cards are restored to the original order. This was made with Processing and Rhino, and then produced by Shapeways.

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Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles. Front view.
Two perfect out-shuffles with thirty-six cards and six piles. Front view.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Two perfect out-shuffles with thirty-six cards and six piles.
Experiment with 90 cards in which a perfect in-shuffle is immediately followed by its inverse. Rendered in Rhino.
Experiment with 90 cards in which a perfect in-shuffle is immediately followed by its inverse. Rendered in Rhino.
Two perfect out-shuffles with thirty-six cards and six piles. Rendered in Rhino.