Category: Complex dynamics

Living technology
Living technology is the field of technology that derives its functionality and usefulness from the properties that make natural organisms alive (see life). It may be seen as a technological subfield
Plotting algorithms for the Mandelbrot set
There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to det
Siegel disc
Siegel disc is a connected component in the Fatou set where the dynamics is analytically conjugate to an irrational rotation.
Julia set
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou
Mandelbrot set
The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/) is the set of complex numbers for which the function does not diverge to infinity when iterated from , i.e., for which the sequence , , etc., remains bounded
Herman ring
In the mathematical discipline known as complex dynamics, the Herman ring is a Fatou component where the rational function is conformally conjugate to an irrational rotation of the standard annulus.
Multibrot set
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 polynom
Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions
No-wandering-domain theorem
In mathematics, the no-wandering-domain theorem is a result on dynamical systems, proven by Dennis Sullivan in 1985. The theorem states that a rational map f : Ĉ → Ĉ with deg(f) ≥ 2 does not have a wa
Periodic points of complex quadratic mappings
This article describes periodic points of some complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a quadratic map is one that inv
In computational and mathematical biology, a biological lattice-gas cellular automaton (BIO-LGCA) is a discrete model for moving and interacting biological agents, a type of cellular automaton. The BI
Complex system
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as
Complex quadratic polynomial
A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.
Filled Julia set
The filled-in Julia set of a polynomial is a Julia set and its interior, non-escaping set
Classification of Fatou components
In mathematics, Fatou components are components of the Fatou set. They were named after Pierre Fatou.