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

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Glossary - I

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IFS     An iterated functional system; it constructs a fractal by iterating a vector quantity through an affine equation that is randomly selected on each iteration.

Imaginary Number     The square root of a negative number. The square root of -1 is often denoted as i for the purpose of writing out complex numbers.

Implicit Parallelism     The idea that genetic algorithms have an extra built-in form of parallelism that is expressed when a GA searches through a search space. Implicit parallelism depends on the similarities and differences between individuals in the population. The theory posits that GAs process more schemata than there are strings in a population, thus getting something of a free lunch. See also no free lunch.

Incomputable     Something that cannot be characterized by a program that always halts. Sets that are incomputable may be recursively enumerable (like the halting set), co-recursively enumerable (e.g., the halting set's complement), or not recursively enumerable (which, if also not CO-RE, is a random set).

Incomputable Number     A real number with an infinite decimal (or binary) expansion that cannot be enumerated by any universal computer.

Inheritable     Refers to a trait that can be genetically passed from parent to offspring.

Inhibitory     Refers to a neural synapse or weight that is negative such that activity in the source neuron encourages inactivity in the connected neuron. The opposite of excitatory.

Inner Product     For two vectors of the same dimensionality, the sum of the pairwise products of the two vector components.

Integral     The cumulative continuous sum of a function. The integral of a differential equation represents the future state of a dynamical system; however, most integrals do not have an analytical solution, which means that they may only have numerical solutions, an admittedly inexact process.

Integration     The act of calculating an integral, by either a numerical or an analytical solution; the inverse operation of differentiation.

Invertible     A function is invertible (with a unique inverse) if the output uniquely determines the input (i.e., it is one-to-one) and the set of legal outputs is equal to the set of legal inputs. The function x^2 is not strictly invertible, while x^3 has an inverse. For operations the definition is slightly looser. While integration and differentiation are considered to be inverse operations, there are an infinite number of integrals that are valid results for integrating any function; thus, the process is not one-to-one.

Irrational Number     A real number that cannot be represented as a fraction.

Iterated Prisoner's Dilemma     The Prisoner's Dilemma game played in an iterative manner for a number of rounds that is unknown to both players.

Iterate/Iterative     Doing something repeatedly. Doing something repeatedly. Doing something repeatedly. Doing something repeatedly. Doing something repeatedly.

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