Tiling involves filling a plane or space with repeated elements, known as tiles. This simple concept is deeply embedded in the natural world and human design, appearing in structures as varied as the hexagonal wax cells of a beehive and decorative wallpapers. While regular hard tiles—geometric shapes with straight edges that fit together without gaps or overlaps—are common in human-made designs, nature often favours soft or irregular patterns, shaped by physical forces. In this lecture, I will explore how both regular and irregular tiling patterns, hard and soft, emerge in nature and the underlying mathematical principles that govern their formation.

This lecture was recorded by Alain Goriely on the 28th of April 2026

Alain Goriely is a mathematician with broad interests in mathematical methods, mechanics, sciences, and engineering. He is well known for his contributions to dynamical systems, mathematical biology, as well as fundamental and applied mechanics. He is particularly well known for the development of a mathematical theory of biological growth, culminating with his seminal monograph The Mathematics on Mechanics of Biological Growth (2017).

He received his PhD from the University of Brussels in 1994 where he became a lecturer. In 1996, he joined the University of Arizona where he established a research group within the renowned Program of Applied Mathematics. In 2010, he joined the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and fellow of St. Catherine’s College. He is currently the Director of the Oxford Centre for Industrial and Applied Mathematics.

In addition, Alain has enjoyed scientific outreach based on problems connected to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, brain modelling, and he is the author of a Very Short Introduction to Applied Mathematics (2017). His work has been recognized by a Sloan Fellowship, a Royal Society Wolfson Research Award, the Cozzarelli Prize from the National Academy of Sciences and the Engineering Medal from the Society of Engineering Sciences. He was elected as a Fellow of the Royal Society in 2022.

The transcript of the lecture is available from the Gresham College website: https://www.gresham.ac.uk/watch-now/shape-tiles

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