Anne Burns
I began my studies as an art major, but switched to mathematics. When I went to my first conference on fractals I was hooked. Visualizing mathematical concepts allowed me to combine both of my interests.
The streamlines of the vector field dx/dt = x^2 - y^2, dy/dt = 2xy (the real and imaginary parts of the complex function f(z) = z^2 ) are the directed paths along which the tangent vector is equal to (dx/dt, dy/dt). They are circles tangent to the real axis. the attached vectors are colored according to their slope.
I will never tire of the endless variations on Mandelbrot's "Basilica". Here we have added a term c/ z^2(z -1)^2 to the function f(z) = z^2-1 and rendered the Julia Set.