The properties of a composite material can sometimes be strikingly different from the constituent materials. The beautiful red glass one sees in old church windows is a suspension of small gold particles in glass. Most materials, such as rubber, get thinner when they are stretched, but it is possible to design composites which get fatter as they are stretched.
Sound waves travel slower in bubbly water than in either water or air.
This lecture explores the range of behaviors a composite can exhibit and describes structures which produce extreme or unusual behavior. These discoveries and related questions involve a rich interplay between mathematics, numerical simulation, and intuition.