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

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Glossary - F

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Feedback     A loop in information flow or in cause and effect.

Feedback Neural Network     A neural network that has every neuron potentially connected to every other neuron. The activations of all neurons are updated in parallel (synchronous or asynchronous order), unlike a feedforward or recurrent neural network.

Feedforward Neural Network     A neural network that is organized with separate layers of neurons. Connections in such a network are limited to one direction such that the activations of the input neurons are updated first, followed by any hidden layers, and then finished with the outputs.

Feigenbaum Constant     A constant number that characterizes when bump-like maps such as the logistic map will bifurcate.

Finite-State Automaton (FSA)     The simplest computing device. Although it is not nearly powerful enough to perform universal computation, it can recognize regular expressions. FSAs are defined by a state transition table that specifies how the FSA moves from one state to another when presented with a particular input. FSAs can be drawn as graphs.

Fish     A simple object in Conway's Game of Life that swims vertically or horizontally.

Fitness     A measure of an object's ability to reproduce viable offspring.

Fitness Landscape     A representation of how mutations can change the fitness of one or more organisms. If high fitness corresponds to high locations in the landscape, and if changes in genetic material are mapped to movements in the landscape, then evolution will tend to make populations move in an uphill direction on the fitness landscape.

Fixed Point     A point in a dynamical system's state space that maps back to itself, i.e., the system will stay at the fixed point if it does not undergo a perturbation.

Formal System     A mathematical formalism in which statements can be constructed and manipulated with logical rules. Some formal systems are built around a few basic axioms (such as Euclidean geometry) and can be expanded with theorems that can be deduced through proofs.

Fractal     An object with a fractal dimension. Fractals are self-similar and may be deterministic or stochastic. See also Cantor Set, Diffusion Limited Aggregation, IFS, Julia Set, L-Systems, MRCM, Mandelbrot Set, and Strange Attractor.

Fractal Dimension     An extension of the notion of dimension found in Euclidean geometry. Fractal dimensions can be non-integer, meaning that objects can be ``more than a line but less than a plane'' and so on. There is more than one way of computing a fractal dimension, one common type being the Hausdorff-Besicovich dimension. Roughly speaking, a fractal dimension can be calculated as the quotient of the logarithm of the object's size and the logarithm of the measuring scale, in the limit as the scale approaches 0. Under this definition, standard Euclidean objects retain their original dimension.

Function     A mapping from one space to another. This is usually understood to be a relationship between numbers. Functions that are computable can be calculated by a universal computer.

Function Approximation     The task of finding an instance from a class of functions that is minimally different from an unknown function. This is a common task for neural networks.

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