A Parade of Surfaces

a pictorial introduction to singularity theory

This page and its links present a pictorial introduction to singularity theory. You'll find examples of many of the surface which occur in singularity theory. There is also a link to the basic definition which you'll need to understand the mathematics behind the theory.

As well as GIF pictures we also have some 3D models, in Virtual Reality Modelling Language VRML format.

• When things go weird! No maths at all is needed to follow this introduction to the subject.
• The Bottom of a Tea-Cup Singularities are everywhere. Here is an example you see everyday.
• When things go weird revisited. A slightly more rigorous introduction. Only a little maths is needed.
• Smooth and Singular Here we give proper mathematical definitions of what we mean by smooth and singular maps.
• Stable Maps and Unfoldings
• Caustics and maps from R^2 to R^2.
• Duals of surface.
• Binary Differential Equations.
• Unfoldings and the ADE classification

Time for a bit of an advert. All the pictures and 3D models were constructed using the Liverpool Surface Modeling Package which I have written. This package can create both parametrised and implicit surfaces and whats more get the singularities right.

You can actually try out some 3D surfaces over the web.

You might like to have a look at some of my Papers which discuss drawing algrbraic varieties/ implicit surfaces, all you ever wanted to know about third order features of surfaces and a general discussion on drawing mathematical objects.