Paradigms for Patterns: Turing’s Instability and Mandelbrot’s Geometry, a talk by Dr James Christian (University of Salford)
Annual Sixth Form Lecture
Abstract
The universe has, at its core, feedback loops for creating patterns. We are surrounded by these patterns every day: from spots and stripes and honeycombs, to trees and clouds and landscapes. Indeed, such structures are so commonplace that we are often oblivious to their presence. This talk will show how Nature’s patterns originate at a mathematical level, starting with the seminal work of Alan Turing from 1952. Turing’s mechanism for predicting the spontaneous emergence of pattern from uniformity is often eclipsed by his more renowned work on code-breaking and computing, but it is no less important scientifically. The concept of a fractal, as pioneered by Benoit Mandelbrot and others, will also be introduced. Fractals force us to rethink some intuitive ideas from Euclidean geometry, particularly when describing complex patterns and structures occurring in the natural world. The talk concludes with interactive hands-on demonstrations of pattern formation in video feedback experiments.
About the Speaker
James Christian has been a Lecturer at the University of Salford since 2011. He is a theoretical physicist and spends his spare time preoccupied by mathematics and playing with fractals just for the fun of it. His current research interests span a curious blend of linear and nonlinear problems including electromagnetic scattering on complex domains, mathematical fluid dynamics, spontaneous pattern formation, and soliton theory. Teaching-wise, he lectures on both the Physics and Mathematics degree programmes.
Registration
For further information, please contact David Naughton or Rachel Stenhouse.
To register for the talk, please contact David Naughton. This event will take place in person at the Manchester Grammar School, and will also be broadcast online via Zoom.
Open to all and especially sixth form mathematics students. No charge is made to attend meetings. Non-IMA members are welcome.
