A set of complex numbers which do not converge to any limit when a given mapping is repeatedly applied to them. In some cases the result is a connected fractal set.

‘Yoccoz has developed a method of combinatorial study of Julia sets and Mandelbrot sets - called ‘Yoccoz puzzles ‘- which permit deep insight.’

‘In 1980, Mandelbrot has discovered the set M of parameter values c for which Julia sets are connected.’

‘The spectrum yields a classic fractal object called a Julia set.’

‘Add to that the fact that the set serves as an index into the variety of Julia sets which, in turn, are classified according to the location of a single parameter inside the Mandelbrot set.’

‘H Cremer produced an essay on his work which included the first visualisation of a Julia set.’

Origin

1970s named after Gaston M. Julia (1893–1978), Algerian-born French mathematician.

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