One simple equation can generate a vast diversity of natural shapes, a Belgian biologist has discovered. The Superformula, as its creator Johan Gielis has christened it, produces everything from simple triangles and pentagons, to stars, spirals and petals. ... The Superformula is a modified version of the equation for a circle1. Changing one term in the formula varies the proportions of the shape - moving from a round circle to a long and skinny ellipse. Changing another varies the axes of symmetry - shifting from a circle to triangle, square, pentagon and so on. Varying both proportion and symmetry together produces shapes with any number of sides, regular and irregular. It can also produce three-dimensional structures, and non-biological shapes such as snowflakes and crystals. "It's a new way of describing nature," says Gielis.