Note (a) for A Universal Cellular Automaton

Emulating Other Systems with Cellular Automata…An example of a mobile automaton (see page 71 ) being emulated by a cellular automaton. … The rules for the mobile automaton and the cellular automaton are shown above. In the rules for the cellular automaton, indicates a cell of any color.

Emulating Other Systems with Cellular Automata…Emulating Other Systems with Cellular Automata The previous section showed that a particular universal cellular automaton could emulate any possible cellular automaton. … As a first example of this, the picture on the facing page shows how a cellular automaton can be made to emulate a mobile automaton. The main difference between a mobile automaton and a cellular automaton is that in a mobile automaton there is a special active cell that moves around from one step to the next, while in a cellular

Emulating Other Systems with Cellular Automata…An example of a Turing machine being emulated by a cellular automaton. … The rules for the Turing machine and the cellular automaton are shown above. In the rules for the cellular automaton, indicates a cell of any color.

Emulating Other Systems with Cellular Automata…From the previous section we know that any cellular automaton can be emulated by a universal cellular automaton. But now we see that a universal cellular automaton is actually much more universal than we saw in the previous section . … A cellular automaton set up to emulate random-access memory in a computer.

Emulating Other Systems with Cellular Automata…And at the outset one might not imagine that such a system could ever readily be emulated by a cellular automaton. … The basic idea is to have the cellular automaton produce a pattern that expands and contracts on each side in a way that corresponds to the incrementing and decrementing of the sizes of numbers in the first and second registers of A cellular automaton set up to emulate a sequential substitution system. The cellular automaton involves 28 colors and nearest-neighbor rules.

Computations in Cellular Automata…And as an example the pictures below show a cellular automaton that computes the square of any number. … A cellular automaton that computes the square of any number. The cellular automaton effectively works by adding the original number n together n times.

Note (a) for The Rule 110 Cellular Automaton

Computations in Cellular Automata…The rule for this cellular automaton is somewhat complicated—it involves a total of sixteen colors possible for each cell—but the example demonstrates the point that in principle a cellular automaton can compute the primes. A cellular automaton constructed to compute the prime numbers. … The rule for the cellular automaton shown here involves 16 possible colors for each cell.

Emulating Other Systems with Cellular Automata…An example of a register machine being emulated by a cellular automaton. The cellular automaton has 12 possible colors for each cell. … Repeated multiplication by 3 in base 2 being performed by a cellular automaton with 11 colors.