Cellular Automata Transforms describes a new approach to using the
dynamical system, popularly known as cellular automata (CA), as a tool
for conducting transforms on data. Cellular automata have generated a
great deal of interest since the early 1960s when John Conway created
the `Game of Life'. This book takes a more serious look at CA by
describing methods by which information building blocks, called basis
functions (or bases), can be generated from the evolving states. These
information blocks can then be used to construct any data. A typical
dynamical system such as CA tend to involve an infinite possibilities of
rules that define the inherent elements, neighborhood size, shape,
number of states, and modes of association, etc. To be able to build
these building blocks an elegant method had to be developed to address a
large subset of these rules. A new formula, which allows for the
definition a large subset of possible rules, is described in the book.
The robustness of this formula allows searching of the CA rule space in
order to develop applications for multimedia compression, data
encryption and process modeling.
Cellular Automata Transforms is divided into two parts. In Part I the
fundamentals of cellular automata, including the history and traditional
applications are outlined. The challenges faced in using CA to solve
practical problems are described. The basic theory behind Cellular
Automata Transforms (CAT) is developed in this part of the book.
Techniques by which the evolving states of a cellular automaton can be
converted into information building blocks are taught. The methods
(including fast convolutions) by which forward and inverse transforms of
any data can be achieved are also presented.
Part II contains a description of applications of CAT. Chapter 4
describes digital image compression, audio compression and synthetic
audio generation, three approaches for compressing video data. Chapter 5
contains both symmetric and public-key implementation of CAT encryption.
Possible methods of attack are also outlined. Chapter 6 looks at process
modeling by solving differential and integral equations. Examples are
drawn from physics and fluid dynamics.
