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Dr. Jason Bramburger writes about the mathematics of patterns and waves

July 4, 2023
By Christopher Plenzich

"Patterns and Waves in Theory, Experiment, and Application" by Dr. Jason Bramburger, from our very own Department of Mathematics and Statistics, is an engaging article aimed at high school students and above, offering a glimpse into the world of patterns and waves found in nature. The article, published in “Snapshots of modern mathematics from Oberwolfach” is unique in that the Dr. Bramburger aptly avoids the use of equations in his explanation, making it accessible to a broader audience. The article explores various types of patterns and waves, including space-filling patterns, localized patterns, spreading waves, and rotating waves. Dr. Bramburger continues by highlighting the significance of these mathematical models in describing biological, chemical, physical, and social processes.


From the article:

In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social processes. We begin by focussing on two types of patterns that do not change in time: space-filling patterns and localized patterns. We then discuss two types of waves that evolve predictably as time goes on: spreading waves and rotating waves. All our examples are motivated with real-world applications and we highlight some of the main lines of research that mathematicians pursue to better understand them.

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