In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is ‘regular’, while on the Julia set its behavior is ‘chaotic‘.
The Julia set of a function f is commonly denoted J(f), and the Fatou set is denoted F(f). These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.
Computer science (abbreviated CS or CompSci) is the scientific and practical approach to computation and its applications. It is the systematic study of the feasibility, structure, expression, and mechanization of the methodical processes (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information, whether such information is encoded in bits and bytes in a computer memory or transcribed engines and protein structures in a human cell. A computer scientist specializes in the theory of computation and the design of computational systems.
Its subfields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory (which explores the fundamental properties of computational problems), are highly abstract, while fields such as computer graphics emphasize real-world visual applications. Still other fields focus on the challenges in implementing computation. For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use ofprogramming language and complex systems. Human-computer interaction considers the challenges in making computers and computations useful, usable, and universally accessible to humans.
In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker in 1992, based on ideas by Uffe Engberg and Mogens Nielsen. It can be seen as a continuation of Milner’s work on the process calculus CCS (Calculus of Communicating Systems). The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation.
The π-calculus is elegantly simple yet very expressive. Functional programs can be encoded into the π-calculus, and the encoding emphasises the dialogue nature of computation, drawing connections with game semantics. Extensions of the π-calculus, such as the spi calculus and applied π, have been successful in reasoning about cryptographic protocols. Beside the original use in describing concurrent systems, the π-calculus has also been used to reason about business processes and molecular biology.