Date started: September 2019

Leads: Roger Antonsen

Abstract

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.

Media

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.

The same object, rendered in Rhino.

Extending this to more cards and more piles, gives the following, which I did not 3D print (yet):

Two perfect out-shuffles with hundred cards and ten piles. Rendered in Rhino.

Experiment with 90 cards in which a perfect in-shuffle is immediately followed by its inverse. Rendered in Rhino.

References

• Roger Antonsen, Eight Ways to Shuffle Sixty-Four Cards, https://rantonse.no/en/art/2018-07-25
• Roger Antonsen, Card Shuffling Visualizations, Proceedings of Bridges 2018, http://archive.bridgesmathart.org/2018/bridges2018-451.html