ABSTRACT
This chapter suggests that elementary catastrophes as described by mathematicians. It explains how the Zeeman catastrophe machine can be used to demonstrate the cusp catastrophe. Parallels are drawn between this machine and a four-pin soap-film model which can be described by a double-cusp catastrophe. The chapter aims to phase transitions and draws parallels between phase-transition theory and catastrophe theory. The cusp catastrophe model involves two control variables and one state variable. It is not strictly applicable to the two-dimensional soap-film patterns under consideration. The configurations or soap-film patterns can be defined by stating the coordinates of the junctions between the separate components of the soap film. When the film pattern changes, the positions and even the number of junctions between components change. The chapter explores a model which allows movement of both the control pin and the film junction in two directions.
