User:GUYTU6J/Life extensions

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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.

Annotation

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.

Rule ? ?
? ? ?

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
LifeHistory state ? /
ExtendedLife state ? state ?
StateInvestigator ? ?
x=8, y = 8, rule = B2n3-k4jkqw5er6i/S23-q4c 2b2o$2bo$2b2o2b2o$b2o3bo$obo$2o$4b2o$4b2o! #C [[ THUMBNAIL THUMBSIZE 3 AUTOSTART GPS 10 LABEL 4 0 9 "To be completed..." ]] #C [[ COLOR BACKGROUND 30 100 190 COLOR ALIVE 255 255 255 ]]