Over the years, a variety of multistate rules based on regular two-state Life have been developed. They have additional states for annotation and modification of evolution. This page catalogs these rules and states.
To annotate a Life pattern is to use different icons (including colours and shapes) to mark cells while preserving the evolution. LifeHistory is the most common Life extension with markers for ON and OFF cells. LifeSuper is a broader rule supporting much more annotations.
Modification of evolution
To modify the evolution of a Life pattern is to affect births and survivals; usually a central, state n>1 cell interacts with the neighbouring, state 0 (OFF) and/or state 1 (ON) cells isotropically.
There are two kinds of interactions. Weak interactions allow neighbouring OFF and ON cells to evolve similarly to the Life rule, and the central cell participate by mimicking either an ON cell or an OFF cell. Strong interactions force or disable the evolution of neighbouring OFF and ON cells in some predefined manner.
How many states are possible? For the 3rd and the 4th columns in Table 1 (a cell's influence on an OFF cell), there are four valid options: both "allowed, OFF-like", both "allowed, ON-like", "disabled & forced" or "forced & disabled". So do the 5th and the 6th columns dealing with influence on an ON cell. Consequently a total of 4×4=16 states are possible. But some reductions can be made. ...
The central cell is usually stable (period-1), but it may also toggle between different states with different properties.
Table 1: state properties
|Index||Common name||OFF to OFF||OFF to ON||ON to OFF||ON to ON||Period||Note|
|1||placeholder||allowed, OFF-like||allowed, OFF-like||allowed, OFF-like||allowed, OFF-like||1||eternal off|
|2||?||allowed, OFF-like||allowed, OFF-like||allowed, ON-like||allowed, ON-like||1||?|
|3||?||allowed, ON-like||allowed, ON-like||allowed, OFF-like||allowed, OFF-like||1||?|
|4||survivor||allowed, ON-like||allowed, ON-like||allowed, ON-like||allowed, ON-like||1||eternal on|
|5||killer||allowed, OFF-like||allowed, OFF-like||forced||disabled||1||for stable boundary|
|6||?||allowed, OFF-like||allowed, OFF-like||disabled||forced||1||?|
|7||killer||allowed, ON-like||allowed, ON-like||forced||disabled||1||for stable boundary|
|8||?||allowed, ON-like||allowed, ON-like||disabled||forced||1||?|
|9||inverter||disabled||forced||forced||disabled||1||inverts all neighbouring cells|
|10||spawner||disabled||forced||allowed, ON-like||allowed, ON-like||1||give birth to off cells|
Table 2: state correspondance in different rules
|Rule||Index 1||Index 2|
|ExtendedLife||state ?||state ?|