chapter 3 - the world of simple programs wolfram, stephen. a new kind of science. wolfram media,...

Chapter 3 - The World of Simple Programs

Wolfram, Stephen. A New Kind of Science. Wolfram Media, Inc. 2002.

www.xiscanoe.org

the search for general features

• Há padrões comportamentais entre os autômatos?

• Há um número ilimitado de padrões?

• O número de padrões é finito? É enumerável?

totatilistic automatas

• the idea of a totatilistic rule is to take the new color of each cell to depend only on the average color of neighboring cells, and not on their individual colors.

mobile automata

• A class of automata similar to cellular automata but which have a single "active" cell instead of updating all cells in parallel. In a mobile automaton, the evolution rules apply only to the active cell, and also specify how the active cell moves from one generation to the next. All cells that are not active remain the same from one generation to the next. Mobile automata can therefore be considered a hybrid between elementary cellular automata and Turing machines.

automatas as turing machines

• A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave the first construction for a universal Turing machine (Turing 1937, 1938). Shannon (1956) showed that two colors were sufficient, so long as enough states were used. Minsky (1962) discovered a 7-state 4-color universal Turing machine, illustrated above (Wolfram 2002, p. 706). Note that the 20th rule specifies that the Turing machine should halt, as indicated by leaving the head stationary and not changing its state. Upon conversion to a 2-color machine, Minsky's universal Turing machine requires 43 states.

other machines

• Substitution systems

• Tag Systems

• Register Machines

• Symbolic Systems!!