The Computational Beauty of Nature
Computer Explorations of Fractals, Chaos,
Complex Systems, and Adaptation

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Glossary - C

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Cantor Set     A simple fractal set composed of an uncountable infinity of dust-like points, but that also has 0 measure (meaning that the sum width of all points is 0). The Cantor set is constructed by removing the middle third of a unit line segment, and then recursively removing the middle third of any remaining line segments, for an infinite number of steps.

Cellular Automaton (CA)     A discrete dynamical system that is composed of an array of cells, each of which behaves like a finite-state automaton. All interactions are local, with the next state of a cell being a function of the current state of itself and its neighbors. Conway's Game of Life is a CA.

Chaos/Chaotic     Irregular motion of a dynamical system that is deterministic, sensitive to initial conditions, and impossible to predict in the long term with anything less than an infinite and perfect representation of analog values.

Chomsky Hierarchy     Four classes of languages (or computing machines) that have increasing complexity: regular (finite-state automata), context-free (push-down automata), context-sensitive (linear bounded automata), and recursive (Turing machines).

Classifier     A rule that is part of a classifier system and has a condition that must be matched before its message (or action) can be posted (or effected). The strength of a classifier determines the likelihood that it can outbid other classifiers if more than one condition is matched.

Classifier System     An adaptive system similar to a Post production system that contains many ``if ... then'' rules called classifiers. The state of the environment is encoded as a message by a detector and placed on the message list from which the condition portion of the classifiers can be matched. ``Winning'' classifiers can then post their own messages to the message list, ultimately forming a type of computation that may result in a message being translated into an action by an effector. The strengths of the classifiers are modified by the bucket brigade algorithm, and new rules can be introduced via a genetic algorithm.

Coevolution     Two or more entities experience evolution in response to one another. Due to feedback mechanisms, this often results in a biological arms race.

Complement     A set composed of all elements that are not members of another set.

Combinatorial Optimization     A class of problems in which the number of candidate solutions is combinatorial in size. Each possible solution has an associated cost. The goal is to find the solution with the lowest cost. Because of the vast numbers involved, explicit search an entire search space is not always possible.

Complete     Describes a formal system in which all statements can be proved as being true or false. Most interesting formal systems are not complete, as proved in Gödel's Incompleteness Theorem.

Complex Number     A number that has a real component and an imaginary component and is characterized as a point on a plane (instead of the real number line).

Complex System     A collection of many simple nonlinear units that operate in parallel and interact locally with each other so as to produce emergent behavior.

Complexity     An ill-defined term that means many things to many people. Complex things are neither random nor regular, but hover somewhere in between. Intuitively, complexity is a measure of how interesting something is. Other types of complexity may be well defined; see the index for other references.

Compressible     Having a description that is smaller than itself; not random; possessing regularity.

Computable     Expressible as a yes/no question that can be answered in any case by a computer in finite time.

Computation     The realization of a program in a computer.

Connectivity     The amount of interaction in a system, the structure of the weights in a neural network, or the relative number of edges in a graph.

Conservative System     A dynamical system that preserves the volume of its state space under motion and, therefore, does not display the types of behavior found in dissipative systems.

Consistence     In formal systems, having the property that all statements are either true or false.

Continuous     Taking a real value, i.e., not discrete. Dynamical systems may operate in continuous time or space.

Control     Exerting actions to manipulate a system or environment in a goal-seeking manner.

Convergence     For computers, halting with an answer; for dynamical systems, falling into an attractor; for searches (e.g., backpropagation and genetic algorithms), finding a location that cannot be improved upon; for infinite summations, approaching a definite value.

Conway's Game of Life     A cellular automaton rule set that operates on a two-dimensional grid. Each cell changes its state according to the states of its eight nearest neighbors: dead cells come alive with exactly three live neighbors, and cells die if they have anything but two or three neighbors. The Game of Life can display complex patterns such as gliders, fish, and glider guns, and is also capable of universal computation.

Co-Recursively Enumerable (CO-RE)     The complement of a set that can be recursively enumerated.

Countable Infinity     Having the same number of objects as the set of natural numbers.

Crossover     A genetic operator that splices information from two or more parents to form a composite offspring that has genetic material from all parents.

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Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002