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- Stephen Wolfram
- 2002

Early in the 1980s Stephen Wolfram began to work in earnest upon cellular automata. These are a class of computer model which may be visualized as a set of memory locations, each containing one bit. These bits are updated in a succession of time steps. In each step, the new value of each bit depends upon the values of neighboring bits. Wolfram particularly… (More)

- Stephen Wolfram
- 1988

Mathematica is a powerful software package that, as the name suggests, allows you to do mathematics on a computer. It may be used as a sophisticated calculator, as we’ll be doing here, or as a programming language. In the latter mode it contains the main elements from several other programming languages but is specifically designed to perform mathematical… (More)

- Stephen Wolfram
- 1996

- Stephen Wolfram
- 2003

- Stephen Wolfram
- 2002

Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit… (More)

- Stephen Wolfram
- 1999

- Stephen Wolfram
- CRYPTO
- 1985

- Stephen Wolfram
- 1991

- Stephen Wolfram
- 2009

Natural systems from snowflakes to mollusc shells show a great diversity of complex patterns. The origins of such complexity can be investigated through mathematical models termed `cellular automata'. Cellular automata consist of many identical components, each simple, but together capable of complex behaviour. They are analysed both as discrete dynamical… (More)

Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The… (More)