Complex dynamicsComplex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety to itself. The related theory of arithmetic dynamics studies iteration over the rational numbers or the p-adic numbers instead of the complex numbers.
Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
Complex systemA 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 power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.
FractalIn mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.
Complex adaptive systemA complex adaptive system is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It is adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events. It is a "complex macroscopic collection" of relatively "similar and partially connected micro-structures" formed in order to adapt to the changing environment and increase their survivability as a macro-structure.
Fractal analysisFractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science.
Benoit MandelbrotBenoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
LacunarityLacunarity, from the Latin lacuna, meaning "gap" or "lake", is a specialized term in geometry referring to a measure of how patterns, especially fractals, fill space, where patterns having more or larger gaps generally have higher lacunarity. Beyond being an intuitive measure of gappiness, lacunarity can quantify additional features of patterns such as "rotational invariance" and more generally, heterogeneity. This is illustrated in Figure 1 showing three fractal patterns.
Primitive data typeIn computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, "primitive data types" may refer to the standard data types built into a programming language (built-in types).
Data typeIn computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data.
