Catastrophe Set of the Plane Projection of a Movable Surface
This Demonstration shows the catastrophe set of the plane projection from the surface. You can rotate the surface by dragging the locator. Observe that the cusp type is the only shape that appears for the catastrophe sets.[more]
Initially, the surface is given by the image of the map . The projection is given by ). The catastrophe set (red curve) is defined by the image of the projection of the discriminant set (blue curve) on the surface, where the surface has vertical tangent lines, or, to be more colloquial, the places on the surface where a walker would fall to a fold directly below or could jump up to a fold directly above.[less]
The theory of Catastrophe Set of the Plane Projection of a Movable Surface in  and .
 V. I. Arnold, S. M. Gusein–Zade, and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Boston: Birkhäuser, 1985.
 T. Bröcker, Differentiable Germs and Catastrophes, London: Cambridge University Press, 1975.
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"Catastrophe Set of the Plane Projection of a Movable Surface"
Wolfram Demonstrations Project
Published: February 23 2010