Julia set

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Related to Julia Sets: Mandelbrot sets

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 construction of the Julia sets (the radii of convergence) corresponding to them, for a detailed study of the type of convergence.
We [22] extended the above results and studied the radial distribution of Julia sets of the derivatives of entire solutions of equations (4) and (5).
Note that the Julia set of a nonlinear map R(z), denoted J(R), is the closure of the set of its repelling periodic points.
Orbits and the Julia set. Australian Senior Mathematics Journal, 16 (2), 53-54.
singular measures, Fourier transform, orthogonal polynomials, almost periodic Jacobi matrices, Fourier-Bessel functions, quantum intermittency, Julia sets, iterated function systems, generalized dimensions, potential theory
Many mathematicians have already contributed to the detailed investigation of the Mandelbrot set's boundary and its closely related kin, called Julia sets. Indeed, Michael Lyubich of Stony Brook independently obtained proofs, comparable to those of Shishikura, concerning the area of Julia sets.
A hands-on, visual learning environment, the exhibit relies on computer graphics, image processing, video, and lasers to teach such concepts as fractals and Julia sets. The Lab members raised the $750,000 it took to create the show, which features seven stations with between three and nine games.
Julia sets (radii of convergence), which were found for different attractors, had a self-similar pattern, thus forming quasi-fractals.
Julia Sets and Complex Singularities of Free Energies
The topics are periodic points, chaos in one and two dimensions, systems of differential equations, fractals, creating fractal sets, and complex fractals in Julia sets and the Mandelbrot set.
Topics include conformal automorphisms of finitely connected regions, meromophic functions with two completely invariant domains, residual Julia sets of rational and transcendental functions, generalizations of uniformly normal families, fractal measures and ergodic theory of transcendental meromorphic functions, and, of course, Baker domains.
One thinks, for example, of the emergence of complex behaviours from simple rules, explored at length in Wolfram's recent tour de force A New Kind of Science; of the visually astounding mappings of the Mandelbrot and Julia sets; or the analysis of algorithmic complexity and randomness in Chaitins' works.