Julia set


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Julia set

[′jül·yə ‚set]
(mathematics)
For a polynomial, p, with degree greater than 1, the Julia set of p is the boundary of the set of complex numbers, z, such that the sequence p (z), p 2(z), …, pn (z), … is bounded, where p 2(z) = p [p (z)], and so forth.
References in periodicals archive ?
The radius of convergence (Julia set) is an important characteristic of the corresponding basin of attraction.
(a) The Julia set of f has an empty interior if the Fatou set is non-empty.
Since [+ or -] 1 are attractive fixed points of B, so the Julia set ](B) is the boundary of the basins of attraction S(-1) and S(1); that is,
A point [z.sub.0] is in the Julia set if and only if dynamics in a neighborhood of [z.sub.0] shows strong dependence on the starting conditions, so that nearby initial conditions yield to wildly different behavior after a number of full iterations.
A complex number z (or a + ib) is a member of a Julia set, for a given real number c, if z is the first member of a sequence, defined by an iterative function, which remains bounded.
Fig ure 1.3 shows the initial part of the evolution in the case of the usual Bessel functions (for which the measure [micro] is absolutely continuous), and Figure 1.4 displays the same information in the case of a singular continuous Julia set measure.
The Mandelbrot set is closely related to the Julia set. Namely, if the value of the coefficient is inside the main cardioid of the Mandelbrot set, Julia set will represent the misshapen circle.
With the support of her family, friends and boyfriend, Julia set about rebuilding her life and the confidence which played such a big part in it.
Orbits and the Julia set. Australian Senior Mathematics Journal, 16 (2), 53-54.
Armed initially with nothing but a good idea, Julia set off on a path which has since seen her embark on a cheese-making course with the UK's experts, as well as converting the family garage into a custom-made workspace complete with a cheese vat.
Julia set up her business in September with the help of a Business Start-up Grant from South Tyneside Means Business.