An application of catastrophe theory to the behavior of ferromagnets in the partially magnetized state is presented. Magnetic phase transitions induced by crystal anisotropy are studied with the help of a swallowtail manifold. The morphology of the Brown equations of micromagnetics is discussed and a general method of solution outlined. The magnetization paths of powder magnets are discussed with the help of geometrical diagrams that extend those presented first by Preisach in 1935.