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

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Glossary - G

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Game Theory     A mathematical formalism used to study human games, economics, military conflicts, and biology. The goal of game theory is to find the optimal strategy for one player to use when his opponent also plays optimally. A strategy may incorporate randomness, in which case it is referred to as a mixed strategy.

Gaussian     Normally distributed (with a bell-shaped curve) and having a mean at the center of the curve with tail widths proportional to the standard deviation of the data about the mean.

Generalized Delta Rule     Another name for backpropagation.

Genetic Algorithm (GA)     A method of simulating the action of evolution within a computer. A population of fixed-length strings is evolved with a GA by employing crossover and mutation operators along with a fitness function that determines how likely individuals are to reproduce. GAs perform a type of search in a fitness landscape.

Genetic Programming (GP)     A method of applying simulated evolution on programs or program fragments. Modified forms of mutation and crossover are used along with a fitness function.

Glider     A simple object in Conway's Game of Life that swims diagonally through the grid space.

Glider Gun     An object in Conway's Game of Life that builds and emits gliders, which can then be collided in purposeful ways to construct more complicated objects.

Global Minimum (Maximum)     In a search space, the lowest (or highest) point of the surface, which usually represents the best possible solution in the space with respect to some problem.

Gödel Number     A natural number computed via a Gödelization procedure that uniquely corresponds to a string.

Gödelization     A method for mapping arbitrary strings to natural numbers such that the process is one-to-one and invertible. The process usually exploits the properties of prime numbers. Since Gödelization can be defined as a computable function, and since functions can be Gödelized, some functions (or programs) can assert statements about other functions or programs, or themselves.

Gödel's Incompleteness Theorem     Any sufficiently interesting formal system can express true statements for which there can be no proof in the original formal system.

Gödel's Statement     Given the formal statement ``There does not exist any proof for the statement with Gödel number x applied to x,'' which has it own Gödel number, g, Gödel's statement paraphrased is ``There does not exist a proof of the statement with Gödel number g applied to itself.'' Gödel's statement is true, but cannot be proven true in the formal system in which it is constructed, which leads to Gödel's Incompleteness Theorem.

Gradient     A vector of partial derivatives of a function that operates on vectors. Intuitively, the gradient represents the slope of a high-dimensional surface.

Graph     A construct that consists of many nodes connected with edges. The edges usually represent a relationship between the objects represented by the nodes. For example, if the nodes are cities, then the edges may have numerical values that correspond to the distances between the cities. A graph can be equivalently represented as a matrix.

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