Fun with Chaotic Orbits in the Mandelbrot Set

Kerry Mitchell
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 389–392


The orbits of points in the Mandelbrot set can exhibit chaos, if the point is on the boundary and not part of a periodic disk. Chaotic orbits that begin nearby are known to diverge exponentially; this characteristic can be exploited to combine multiple chaotic orbits into one image. Such combinations can be used to investigate the dynamics of the orbit or enjoyed for their own aesthetic sake.