Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in a Buddhist myth: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led in his imagination to remarkable forms with hitherto unknown symmetries.
In the 1980s a group of mathematicians embarked on the first computer exploration of Klein's vision, and in doing so found further extraordinary images of their own. Join one of the group, Caroline Series, on the path from basic mathematical ideas to simple algorithms whose repetition creates delicate fractal filigrees which are only now beginning to be explored fully.
This is the 2010 joint London Mathematical Society / Gresham College lecture.
Caroline Series is a Professor at the Warwick Mathematics Institute at the University of Warwick. Her interests lie in Hyperbolic geometry, Kleinian groups and dynamical systems. One of her recent publications is Indra's Pearls: The Vision of Felix Klein which she co-authored with David Mumford and David Wright.