Trying to remember a piece of cellular automaton jargon

[Bohandas]

IIRC there was a word for the property of cellular automata like Life, High Life, etc. that meant that you only need to know the current state of the system (and not any of the previous ones) to calculate the next state. Does anybody know what the word is that I'm thinking of? I'm gonna go nuts trying to remember it.

[Manga Shoggoth]

Deterministic, perhaps? Although I recall that that is more a system you can predict knowing its initial conditions.

[Quizatzhaderac]

Maybe "time independent"?

Let's say we're simulating a bunch of bouncing balls with Newtonian physics. Each ball, at every instant, has (as a part of it's computer model) a position and a velocity. However it's entirely impossible to observe velocity in a single frame/instant. You can entirely remove velocity from your equations by rewriting vt to st-st-1.

Does the simulation I described have the property you're thinking of?

[ArmyOfOptimists]

This is sometimes referred to as a zero-player game (https://en.wikipedia.org/wiki/Zero-player_game). "A game that evolves as determined by its initial state, requiring no further input from humans is considered a zero-player game."

Deterministic also works. A deterministic system is anything that, given a specific input, will always produce the same output. As long as you know the state of the system at any point and the deterministic rules it follows, you can always calculate exactly where it will end up. It also gets used in games a lot to refer to actions the player can take with non-random outcomes. For instance, an game where a sword attack always does 8 + STR damage and hits anything with less than 10 Defense is deterministic, as opposed to the traditional DnD-like systems that use random dice rolls to shake up outcomes.

[Maat Mons]

A system is considered “Memoryless” if you only need to know the current inputs to calculate the current outputs. However, that basically means the system doesn’t have a meaningful internal state. You seem to be describing the reverse, where there is an internal state that needs to be known, but no external inputs to worry about.

Also, the opposite of “Memoryless” is “Hysteretic,” if you enjoy jargon for describing systems.

[NichG]

Are you thinking of Markovian?

[Chronos]

It's not time-independent, because time independence implies time reversibility, and Life (among others) isn't time-reversible: Given the state at t, you can fully determine the state at t+1, but given t+1, you can't determine t (there could, for instance, have been any number of isolated cells that died last step).

[Sermil]

Stateless or memoryless, maybe?

Totalistic, according to Wikipedia: https://en.wikipedia.org/wiki/Cellular_automaton#Totalistic

[NichG]

Totalistic means that it only cares about the count of cells in its neighborhood rather than their specific pattern. It doesn't have to do with time...

[Devils_Advocate]

"Iterative"?