  Hyperbolic numbers are a variation of complex numbers, but their dynamics is
quite different. The hyperbolic Mandelbrot set for quadratic functions over
hyperbolic numbers is simply a filled square, and the filled Julia set for
hyperbolic parameters inside the hyperbolic Mandelbrot set is a filled
rectangle. For hyperbolic parameters outside the hyperbolic Mandelbrot set, the
filled Julia set has 3 possible topological descriptions, if it is not empty,
in contrast to the complex case where it is always a non-empty totally
disconnected set. These results were proved in [1,2,4,5,6,7] and are reviewed
here
