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Computational Design and Analysis of a Magic Snake.
Zilong Li1, Songming Hou2, Thomas C Bishop3
1Center for Biomedical Engineering and Rehabilitation Science, Center for Applied Physics, Louisiana Tech University, Ruston, LA 71270.
Journal of Mechanisms and Robotics
|June 25, 2021
Summary
This study presents a method to represent the Magic Snake (Rubik's Snake) as a 1D sequence, enabling the computation of all its 3D conformations. This approach has applications in modeling various chain-like structures.
Area of Science:
- Computational geometry
- Toy science
- Mathematical modeling
Background:
- The Magic Snake (Rubik's Snake) is a less-explored puzzle compared to Rubik's Cube.
- The number of possible 3D conformations for the Magic Snake remains unknown, unlike its single 3D structure for Rubik's Cube.
Purpose of the Study:
- To develop a method for representing the Magic Snake as a 1D sequence convertible to 3D structures.
- To devise strategies for designing Magic Snakes with specific 3D conformations.
- To enable the computation of all possible 3D conformations of the Magic Snake.
Main Methods:
- Representing the Magic Snake as a 1D sequence.
- Developing two design strategies: folding onto space curves and "embedding" for expansion.
- Utilizing these methods to list and compute all possible 3D conformations.
Main Results:
- A 1D sequence representation for the Magic Snake was established.
- Two novel strategies for designing specific 3D structures were introduced.
- The study provides a framework for computing all possible 3D conformations.
Conclusions:
- The developed methods allow for the rapid listing and computation of all Magic Snake 3D conformations.
- This approach serves as a foundation for multidimensional representations of chain-like structures, including robots, polymers, proteins, and DNA.
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