Wireworld

Wireworld is a cellular automaton, which was first used in 1987 by Brian Silverman in his program Phantom Fish Tank and later by an article in the column Computer Recreations of Scientific American became more widespread. Wireworld is particularly suitable for the simulation of electronic logic elements such as gates or flip-flops. Despite the simplicity of its rules (see below) Wireworld Turing-complete, means that you can even create full computer (also see web link).

Regulate

A Wireworld cell can supply four different states ( the specified color is used in the animated graphics on this page ):

The time proceeds in discrete steps, so-called generations. In this case, an empty cell is basically empty. The remaining cells behave when passing from one generation to the next as follows:

• From an electron is an electron head end.
• Is a conductor of an electron end.
• Of a conductor, an electron head if exactly one or two of the adjacent cells are electron heads. When adjacent to it the so-called Moore - neighbors, which are all cells surrounding the conductor, the only diagonally adjacent apply.

Applications

Applying these rules to the following arrangement of cells, so the electron moves in every generation one position to the right ( = conductor, electrons end # @ head electrons ):

Generation n ==== @ # ======== Generation n 1 ===== @ # ======= Generation n 2 ====== ====== @ # With the proper head of branches and intersections logic switching elements can be realized by simple gates to complex calculator.

The picture at left shows the implementation of two clock (left half ) and an XOR gate (right). The clock generators are designed as annular conductor paths in which revolve two electrons at different distances. The branches at the right edge of the Rings copies of the electrons are emitted into the conductor tracks leading to the inputs of the XOR gate. The clocks are matched to one another that either each of a single electron from the top or bottom enters the XOR gate ( it is passed ), or two electrons arrive at the gate at the same time - they " annihilate " each other, and at gate output does not occur electron from. So that an XOR operation of the incoming electrons to the gate inputs is realized.

Signals

In World wire, there are various coding for the transmission of data. All have in common that a total signal is divided into blocks of equal length. A coding with the block length n is called " n- Micron " - or "n -tick" coding.

In the so-called real - encoding a logic 0 with an empty block, and a 1 is represented by a block with an electron at the beginning. The minimum block length is in this case 3, since between two electrons at least one field must be always distance. In the Complex encodings is a 1 as usual by an electron at the beginning of the block, a 0 but not by any but represented by a one generation delayed electron. Here, the minimum block length 4 Usually one uses

• 6 -micron Real
• 4 -micron Real
• 4 -micron Complex
• 3 -micron Real

The encodings with lower block size are faster, but may require more complex circuits.