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
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image2-7.jpg?resize=1091%2C1091&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image10-3.jpg?resize=1091%2C724&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image7-3.jpg?resize=1091%2C1091&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image3-6.jpg?resize=1091%2C1091&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image8-3.jpg?resize=1091%2C1091&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image1-6.jpg?resize=1091%2C1091&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image5-4.jpg?resize=1091%2C869&ssl=1)
Extending this to more cards and more piles, gives the following, which I did not 3D print (yet):
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image4-5.jpg?resize=1091%2C891&ssl=1)
![](https://i0.wp.com/im.icerm.brown.edu/wp-content/uploads/2020/01/image9-2.jpg?resize=1091%2C891&ssl=1)
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