Progressive Game State Sculputres – Illustrating Mathematics

Date started: September 2019
Leads: Roger Antonsen, Laura Taalman

Abstract

In this project we explore 3D methods for visualizing a series of game states that show the progression of all moves in a “solution sculpture”, starting with the simple class of peg-jumping games as studied by Beasley and Bell (see references). With Processing code we tracked the movement of each game piece and stored that movement of data exportable to Rhino/Grasshopper for piping and rendering. Each game state is a 2D level in the final game state model. The model can be 3D printed as a physical solution sculpture for futher exploration and visualization. Future applications will include student exploration of game state models in an upcoming independent research class, and extension of these methods to more complex jumping/movement games.

Media

Screenshot from Processing code for implementing and tracking game states in a peg-jumping game (perfect solution shown)

Resulting 3D game state model, piped and rendered in Rhino/Grasshopper

Same game state model but with peg paths encoded by color

Photograph of 3D printed solution sculpture, printed in Nylon at Shapeways (Photo credit: Roger Antonsen)

References

Peg Solitaire resource page by George Bell: http://recmath.org/pegsolitaire/index.html
The Ins and Outs of Peg Solitaire, John Beasley, Oxford University Press, 1985: https://www.amazon.com/Ins-Outs-Solitaire-Recreations-Mathematics/dp/0198532032