Quadratic Polynomials

We are interested in the dependence of a dynamical system on parameters, and we focus on the maps z → z2 + c. This leads to the Mandelbrot set ℳ in parameter space, which has a universal character in the sense that similar-looking sets show up when one studies very general parameter dependence. One striking feature of ℳ is that shapes of certain of the Julia sets ℐ _c in dynamic space (z-space) are reflected in the shape of ℳ near the corresponding points in parameter space (c-space).