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Swallowtail Catastrophe

A Catastrophe which can occur for three control factors and one behavior axis. The equations

$\displaystyle x$ $\textstyle =$ $\displaystyle uv^2+3v^4$  
$\displaystyle y$ $\textstyle =$ $\displaystyle -2uv-4v^3$  
$\displaystyle z$ $\textstyle =$ $\displaystyle u$  

display such a catastrophe (von Seggern 1993, Nordstrand). The above surface uses $u\in [-2,2]$ and $v\in [-0.8, 0.8]$.


Nordstrand, T. ``Swallowtail.''

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 94, 1993.

© 1996-9 Eric W. Weisstein