The Douady rabbit is a Julia set (http://planetmath.org/SetDeJulia) produced by

 $c=-\frac{1}{8}+\frac{3}{4}i.$

As the Mandelbrot set indicates, the real part can be varied to as much as $-.2$ while the imaginary part can be varied to as much as $.75i$ and still produce a connected set.

Title Douady rabbit DouadyRabbit 2013-03-22 17:15:51 2013-03-22 17:15:51 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Example msc 28A80