Visualizing Implicit and Differential Surfaces in Three Dimensions



	First Program: a tool for educators The first program is useful for mathematics educators. Many students study various implicitly describable surfaces in three dimensions, but before development of the first program, tools for visualizing these surfaces were either expensive or of poor quality. The algorithms developed for the first program may also be useful for commercial mathematics applications such as Mathematica or MatLab.

Second program: a tool for researchers The second program will be of more use to mathematics researchers in the field of dynamic systems. To my knowledge, this program is the first visualization tool capable of displaying stable and unstable manifolds for arbitrary systems of differential equations.

	The Lorenz equations The first differential equations that I intend to study are the Lorenz equations. Famous for its butterfly-shaped one-dimensional stable manifold, the Lorenz equations also describe a two-dimensional unstable manifold. Images of this surface exist, but they were produced using a tool specific to the Lorenz equations and not applicable to other systems of equations.

Back to the front page
Written and designed by Adam Barth. February 17, 2000