Tutorials/General technology

Tutorials/General technology

So now, after coming across a good cellular automata, you have decided to do something less abstract with it — something more significant than random soup searching and more engaging than automatic software searching. Then you begin to consider signal circuitry, the very connection between microscopic evolution and macroscopic construction. (Actually, that is approximately what cellular automata were originally created for; the basis of modelling self-replicating systems.)

What is a signal and what do they do?

A signal is a moving configuration different from its background, and thus carrying some information. In terms of cellular automata, the following patterns can serve as signals:

• Spaceships in an empty medium,
• Fuses, drifters and negative spaceships in some nonempty media, and
• Active reactions, particularly methuselahs, in conduits.

A signal travels through the space at a certain speed, which is an important measure since timing (especially synchronization) decides whether signal circuitry works or not.

Signals transform and interact in various ways. A lone signal can be created, reflected and/or flipped, delayed/advanced, multiplicated, transformed into other signal(s), or destroyed. Two or more signals react to annihilate or to perform logic operations. These rely on some devices, namely guns/factorys, reflectors, advancer, pulse dividers, duplicators, converters, eaters, Boolean logic gates, etc.

How to find these building blocks?

Constructing signal circuitry involves both human idea and computer power. Here some simple demonstration may provide hints on how to develop signal circuitry.

Example 1: Conway's Game of Life, with the Gosper glider gun

The signal: glider

Imagine travelling back to the early life days in the 1970s. When tracking the evolution of small polyomino patterns, Life enthusiasts observed a moving configuration as follows:

x=3, y = 3, rule = B3/S23 bo$2bo$3o! #C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 4 LOOP 4 TRACK 0.25 0.25 ]]

Soon the spaceship became known as the glider, and found its part in the signal circuitry. Before constructing anything let's analyze its movement.

A glider travels one cell down and one cell right in four ticks, during which it shows two alternating shapes in a glide-symmetric manner. To reflect these facts we have some terminologies:

Visualization of glider-related concepts

• Phase: the arrangement of cells in one tick. A glider has 4 phases.
• Period: the minimum number of ticks passed to appear in the same phase. A glider is period 4.
• Speed: the displacement in a period divided by period. A glider has speed (1,1)c/4.
• Mod: because the 1st&3rd phase are identical considering reflection and translation, and so does the 2nd&4th, a glider is said to have a mod of 4/2 = 2.
• Lane: the diagonal linear region where a travelling glider has covered or will cover.

Additionally, we will need to define parity and color so as to describe the relationship between two gliders. ...

The signal sink: eater 1

An important question following the discovery of glider is, what can we use when we want to suppress a glider? Fortunately, the following 7-cell fishhook-shaped still life can kill a glider and then recover in four ticks.

x=9, y = 9, rule = B3/S23 bo$2bo$3o3$5b2o$5bobo$7bo$7b2o! #C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 4 LOOP 12 ]]

This is called an eater, a subgroup of catalysts.

The signal source: Gosper glider gun

Since the discovery of glider, people have been seeking for patterns that generates gliders. Later, a sustainable collision between two queen bees was discovered that could yield gliders again and again. This is known as the Gosper glider gun:

x=36, y = 20, rule = B3/S23 24bo$22bobo$12b2o6b2o$11bo3bo4b2o12b2o$10bo5bo3b2o12b2o$2o8bo3bob2o4bo bo$2o8bo5bo7bo$11bo3bo$12b2o$23bo$24b2o$23b2o6$30bobo$31b2o$31bo! #C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 8 LOOP 30 ZOOM 8 ]]

Signal interactions: glider collisions

Next, we want to know how gliders can react with each other. Beginning with the simplest case of two gliders, we enumerated two-glider collisions...

Example 2:

Add your suggestion here (best with other kind of systems, possibly like Banks-I and else)!