The *swallowtail* catastrophe is exemplified by the inflection point of the function `f(x) = x ^{5}` at

The catastrophe locus in the space of parametersa, b, c for the most general perturbation of f(x) = xThe locus separates perturbations with no minimum (green-sided region),perturbations with one minumum (blue-sided region) and perturbationswith two minima (pink-sided region).^{5}. |

The red line is a one-dimensional section of parameter space which, read going upwards, has a process change from one minimum to two minima, then back to one minimum which disappears. The corresponding verb class is |

- 1. Natural languages, human thought and topology
- 2. Thom's axioms
- 3. The simple minimum: ``I am.''
- 4. The fold: ``The day begins.''
- 5. The cusp: ``The fish swallows the bug, '' etc.
- 6. The swallowtail: ``The bird lays an egg, swallows it and dies.''
- 7. Derivatives of the swallowtail: ``She repulses his advances,'' etc.
- References