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...

functions, the boundary of the Mandelbrot set generalizes to the bifurcation locus.[citation needed] The Multibrot set 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...

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 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...

and epicycle Epicyclic gearing Epitrochoid Hypocycloid Hypotrochoid Multibrot set 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...

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....

analogy, the term Misiurewicz point is also used for parameters in a multibrot set where the unique critical point is strictly pre-periodic. This term...

Artur; Lyubich, Mikhail; Shen, Weixiao (2008). "Parapuzzle of the Multibrot set 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 'Multibrot sets'. 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...