Tan Lei was a mathematician specialising in complex dynamics and functions of complex numbers. She is most well-known for her contributions to the study of the Mandelbrot set and Julia set.
Tan Lei in Oberwolfach, 2008
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.
Thus the behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic".
The equipotential lines for iteration towards infinity
Three-dimensional rendering of Julia set using distance estimation
Image: Juliasetsdkfieldlines 1
Image: Juliasetsdkfieldlines 4