Golomb Patterns, Astrophysics, and Citizen Science Games

Abstract

This paper presents an online citizen science game called “Game and Repository for Aperture Solutions and Patterns (GRASP).” GRASP is uniquely tailored to an important task of designing a small-aperture antenna array by leveraging a mathematical structure called the Golomb pattern. In this application of GRASP, an optimal aperture pattern leads to space images of desired spectral resolution observed with the least-cost antenna aperture array via interferometry imaging techniques. Finding near optimal Golomb patterns is computationally very hard. GRASP citizen scientists are tasked with finding (near-)optimal Golomb patterns by selecting cells on a grid that obeys the rules of the game, ensuring Golomb properties to be satisfied. They can also submit known Golomb solutions with their citations, display existing solutions in the GRASP repository, and employ GRASP solutions for non-redundant aperture design of the interferometry and radar applications. In this paper, we introduce the concept of Golomb patterns, and present current design and framework of our citizen science platform GRASP as a means to solve, store, and display such patterns, as well as the motivation behind our work. In particular, we discuss the application of Golomb patterns in astrophysics’ inteferometry missions for small-aperture antenna array design.

Keywords

• Citizen science
• online game
• Golomb rectangles
• Golomb rulers
• Costas arrays
• non-redundant apertures