Multibrot 3 at the bottom-left of the main part.detail of multiJulia 8.Multibrot_4.
Construct in mathematics
Multibrot exponent 0 - 8
In mathematics, a Multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions.[1][2][3] The name is a portmanteau of multiple and Mandelbrot set. The same can be applied to the Julia set, this being called Multijulia set.
where d ≥ 2. The exponent d may be further generalized to negative and fractional values.[4]
^"Definition of multibrots". Retrieved 2008-09-28.
^"Multibrots". Retrieved 2008-09-28.
^Wolf Jung. "Homeomorphisms on Edges of the Mandelbrot Set" (PDF). p. 23. The Multibrot set Md is the connectedness locus of the family of unicritical polynomials zd + c, d ≥ 2
In mathematics, a Multibrotset is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by...
functions, the boundary of the Mandelbrot set generalizes to the bifurcation locus.[citation needed] The Multibrotset is obtained by varying the value of the...
the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function...
and every point not in the Cantor set is in one of these intervals, so its derivative is 0 outside of the Cantor set. On the other hand, it has no derivative...
It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger...
and epicycle Epicyclic gearing Epitrochoid Hypocycloid Hypotrochoid Multibrotset Roulette (curve) Spirograph J. Dennis Lawrence (1972). A catalog of...
Non-fractal imagery may also be integrated into the artwork. The Julia set and Mandelbrot sets can be considered as icons of fractal art. It was assumed that...
iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter. The "chaos game" method plots points in random order all over...
analogy, the term Misiurewicz point is also used for parameters in a multibrotset where the unique critical point is strictly pre-periodic. This term...
pattern or data set (e.g., an image or object) according to a predetermined scanning plan to cover the relevant part of the data set, recording, i.e....
Artur; Lyubich, Mikhail; Shen, Weixiao (2008). "Parapuzzle of the Multibrotset and typical dynamics of unimodal maps". arXiv:0804.2197 [math.DS]. Avila...
corresponding to the Cantor set. A fractal string is the analogue of a one-dimensional "fractal drum," and typically the set Ω{\displaystyle \Omega } has...
z^{d}+c\,} (where d ≥ 3 {\displaystyle d\geq 3\,} ) are often called 'Multibrotsets'. For these families, the bifurcation locus is the boundary of the connectedness...
the attractive cycle Boundaries of level sets Binary decomposition With spine With external rays Multibrot-4 Douady rabbit A Douady rabbit on a red background...
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