**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.