An Exploration Into The Ever-changing Expanse of Non-periodic Tilings

Honors College Thesis

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/honors_college_theses/1n79hd193

Descriptions

Attribute Name	Values
Creator	Tassin, Ian
Abstract	This paper synthesizes various works Wang tiles up to this point, including: the reduction from the Halting Problem to Wang Tiling Problem and notions around various aspects of periodicity, including minimal period, aperiodicity, and axis-aligned periodicity. Additionally it includes new work, including: a proof that a tiling can be periodic without having axis-aligned periodicity, a proof demonstrating the undecidability of the Full-Plane Bounded Use Wang Tiling Problem, proof that if a k-dimensional tiling is periodic in k-1 dimensions it must be periodic in all k-dimensions. This paper also explores Wang tilings in higher dimensions and include code that can be used to test if a given 3D tile set can tile a finite space of a given size. Data and analysis from experiments run with this code is also provided. Finally, this paper includes several novel tile sets, including a 3D set, XOR_{3D}.
Contributor	Bennett, Huck
Resource Type	Honors College Thesis
Date Issued	2023-05-25
Degree Level	Bachelor's
Degree Name	Honors Bachelor of Science (H.B.S.)
Degree Field	Computer Science
Degree Grantor	Oregon State University
Commencement Year	2024
Advisor	Bennett, Huck
Committee Member	Lee, Stefan Nayyeri, Amir Roybal, Roger
Non-Academic Affiliation	Oregon State University. Honors College
Rights Statement	In Copyright - Non-Commercial Use Permitted
Related Items	Ian Tassin Huck Bennett
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

Parents:

This work has no parents.

In Collection:

Title	Date Uploaded	Visibility	Actions
CubeTest.py	2024-01-10	Public	Download
tiling_input.py	2024-01-10	Public	Download
TassinIan2024.pdf	2024-01-17	Public	Download