Extended Generations

Extended Generations rules are a generalization of Generations rules. This extension explores the result of changing the amounts of time cells can be active/inactive for, and also of allowing cells to "come back" from inactivity and alternate between being active/inactive an indefinite amount of times before dying.

They were conceived by users DigitalCross and later Milo Jacquet.[1]

Description

Extended Generations rules are described by rulestrings in the form Bb/Ss/Dd; where b and s are numbers between 0 - 8. The last segment, d, specifies ranges of activity/inactivity, starting with the former and then alternating.

We write n ∈ B, n ∈ S if n is one of the numbers in b, s; patterns then evolve according to the following rules:

1. An active cell
1. Remain in its current state if n ∈ S
2. If not, it advances to state ((x + 1) mod y) in the next generation of the pattern where x is the current state and y is the total number of states.
2. An inactive cell
1. Advances to state ((x + 1) mod y) in the next generation of the pattern where x is the current state and y is the total number of states. I behaves like a normal Generations dying cell.
1. Advances to state 1 if n ∈ B.
2. If not, it remains dead.

Generations and snoitareneG[2][3][4] can be considered subsets of the Extended Generations rulespace.[1]

Software support

Extended Generations rules are not natively supported by either Golly or LifeViewer (support is planned for the latter),[5] but can be run using the Golly's RuleLoader algorithm and a suitable rule table. Catagolue and apgsearch also support Extended Generations rules.

References

1. M. I. Wright (August 1, 2018). "Extended" Generations rules (discussion thread) at the ConwayLife.com forums
2. Saka (July 2, 2017). snoitareneG Rules (discussion thread) at the ConwayLife.com forums
3. Martin Grant (April 10, 2010). "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
4. Brian Prentice (June 4, 2017). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
5. Chris Rowett (January 26, 2019). Re: Pattern viewer for forum threads (discussion thread) at the ConwayLife.com forums