A delay differential equation (dx/dt = (ax(t-tau))/(1 +
x^10(t-tau)) - bx(t)) that can display a wide variety of behaviors
via an adjustable delay term, tau. Even though this system
generates a single scalar time series, it can be extremely
chaotic because its value at any time may depend on its entire
An extremely complex fractal that is related to Julia sets
in the way that it is constructed and by the fact that it acts as a
sort of index to the Julia sets. Like the Julia sets, the Mandelbrot
set is calculated via an iterative procedure. Starting
conditions that do not diverge after an infinite number of
iterations are considered to be inside the set. If, and only if, a
complex number is in the Mandelbrot set, then the Julia set that
uses that complex number as a constant will be connected; otherwise,
the corresponding Julia set will be unconnected.
A function that is usually understood to be iterated in
discrete time steps.
A rectangular two-dimensional array of numbers that can be thought of
as a linear operator on vectors. Matrix-vector
multiplication can be used to describe geometric transformations such
as scaling, rotation, reflection, and translation. They can also
describe the affine transformation used to construct IFS and
The arithmetical average of a collection of numbers; the center of a
A unit of cultural information that represents a basic idea that can
be transferred from one individual to another, and subjected to
mutation, crossover, and adaptation.
The basic unit of information in a classifier system that is
stored in the message list. A message may correspond to an
external state of an environment or an internal state of the
The portion of a classifier system that retains information in
the form of messages.
In game theory, a strategy that uses randomness by
employing different actions in identical circumstances with different
In the sciences, a model is an estimate of how something works. A
model will usually have inputs and outputs that correspond to its
real-world counterpart. An adaptive system also contains an
implicit model of its environment that allows it to change its
behavior in anticipation of what will happen in the environment.
Model of Computation
An idealized version of a computing device that usually has some
simplifications such as infinite memory. A Turing machine, the
lambda calculus, and Post production systems are all models
The property of a function that is always strictly increasing or
strictly decreasing, but never both. The sigmoidal
activation function of a multilayer perceptron is
The Multiple Reduction Copy Machine algorithm, which can be used
to make affine fractals. MRCM fractals are related to
IFS fractals in that they both use the same types of affine
transformations. The MRCM algorithm performs several affine
transformations of a seed image in parallel to yield a secondary
seed image. The output of the MRCM is recursively passed back
through to its input multiple times, to yield the fractal.
Multilayer Perceptron (MLP)
A type of feedforward neural network that is an extension of the
perceptron in that it has at least one hidden layer of
neurons. Layers are updated by starting at the inputs and ending
with the outputs. Each neuron computes a weighted sum of the incoming
signals, to yield a net input, and passes this value through its
sigmoidal activation function to yield the neuron's
activation value. Unlike the perceptron, an MLP can solve
linearly inseparable problems.
A random change in any portion of genetic material. For a
genetic algorithm, this means that a value in a bit
string is randomly set.