World Wide WireWorld
by Nyles Heise

First of all, my thanks to

WireWorld is the famous 2-D cellular automaton created by Brian Silverman in 1987. It was basically presented to the world by A. K. Dewdney in the 1990 issue of Scientific American.

The beauty of WireWorld is that the basic concept is easy to understand, but mastery of design is difficult.

So here's WireWorld. Rectangular grid, each cell is one of 4 states.

  1. Background, always background
  2. Wire, changes to Electron Head if 1 or 2 of its 8 neighbor are Electron Heads
  3. Electron Head, always changes to Electron Tail
  4. Electron Tail, always changes to Wire

From of this definition, logic circuits (and a whole lot more) can be built. I will not not talk much about the well-known designs, but present my 4-tick logic gates and more complex machines. A good source of WireWorld devices can be found at Karl Scherer's Web Site.

I give the designs as gif's or jpg's, but also use the MJCell applet to allow you to watch the devices run. The basic logic gates and some of the smaller machines work well with the applet. The larger machines can be viewed nicely with MJCell, but don't expect them to run to completion. To run the large machines download the mcl files from this web site and run with Mirek's Cellebration. MCell a marvelous, free program. That's right. Marvelous. And Free. All the designs presented here run well in MCell.

My excursions into WireWorld started by reading Mr Dewdney's article in the 1990 issue of Scientific American. I devised 6-tick logic elements, and, after a few sleepless nights, 4-tick methodology. My letter to Mr. Dewdney, which he mentioned in the March issue, was converted into HTML format and is included here.

Many of the basic 4-tick logic gates are presented. Some of these were available in 1990. Others have been recently redesigned to fit into a more compact area. The methodology is the same as in 1990. Some of the new layouts were done by Karl Scherer.

This is the smallest logic gate possible in WireWorld. Guaranteed!

Several versions of 4-tick binary multipliers are given. The design is a offshoot of the work done by Brian Trial, Nick Gardner, and most notably, Karl Scherer.

This is a famous 2D Turing machine. It was the first of several Turing machines I designed.

Ed Pegg Jr. has devised a slight modification to the Langton's Ant rules that makes our ant do a binary count.

Here is a Turing machine that does not have a central control mechanism. It does a binary copy, as given in Karl Scherer's Zillion's Turing Machine.

As far as I know this is the first published WireWorld implementation of a Turing Machine. It does a unary multiply. Two versions are given. This design is presented in MathPuzzle and was awarded a $20 prize as the first WireWorld Turing Machine.

A Turing machine of the first type that does a "big" multiply of 5x8.

Some 3-tick gates, including a very small latch.

A Wireworld implementation of the train set so elegantly espoused by the Tweedle's, Dum and Dee. Actually what's given is a Unary Multiplier (1) in a Turing Machine (2) in a Train Set (3) in WireWorld (4). The highest level of indirection I will attempt.