The Immigration Game: How Two-Color Life Decides Who Owns a Cell

Run a glider into a block in standard Conway's Game of Life and something is born, or isn't, according to one rule: exactly three live neighbors makes a cell live. The new cell doesn't remember which three neighbors did it. It has no history, no owner, no allegiance — it's just on.

In 1971, a Life hobbyist named Don Woods asked a different question: what if a birth kept a receipt? What if every live cell belonged to someone, and a birth's parentage decided who? The rule he came up with — a one-line change now generally known as Immigration — is still the cleanest way anyone has found to turn Life's population into two competing populations. It's also, decades later, the rule we're building our own two-player duel on top of.

The newsletter this actually comes from

Martin Gardner's October 1970 Scientific American column made Life famous, but the day-to-day laboratory for early Life research wasn't Gardner's column — it was a newsletter called LIFELINE. Robert Wainwright, the reader who first verified Bill Gosper's glider gun for Gardner, describes starting it himself:

"In March 1971, with Gardner's encouragement... LIFELINE, a quarterly newsletter for enthusiasts of John Conway's Game of Life, was initiated... Late in 1973, near the end of its third year, LIFELINE ceased publication."

That's from Wainwright's own account, "Conway's Game of Life: Early Personal Recollections," published in Game of Life Cellular Automata (ed. Andrew Adamatzky, Springer-Verlag London, 2010). Eleven issues, eleven quarters, and — according to a 2006 retrospective by Life researchers H. Koenig and Dave Greene on their Game of Life News blog — issue #2 of that newsletter is where Immigration first appeared.

The rule: majority wins, and it can't actually tie

Here's Koenig's description of what Woods proposed:

"Don Woods attempted to come up with a two-person version in which players would have bits of their own color. When different colors resulted in the birth, the majority color (two out of three) would determine the new cell's color."

That's the entire rule. Standard Life's birth condition is untouched — a cell still needs exactly three live neighbors to be born. Immigration only answers a question standard Life never asks: once a birth happens, which color does the new cell get? Look at the three parent cells; whichever color appears at least twice wins.

It's worth noticing why this particular rule needs no tie-breaker. Three parent cells, two possible colors: the only ways to split them are 3–0 or 2–1. There's no way to divide three objects evenly between two groups. Immigration's majority rule isn't a simplification of some messier scheme — for exactly two colors, it's the only outcome the arithmetic allows.

Try it against any known collision and the effect is immediate. Run a glider at a toad with both colored differently, and Koenig's piece notes the wreckage doesn't cleanly belong to one side — collisions routinely leave behind hybrid objects, oscillators or still lifes built from cells of both colors, all the way down to the single-cell level. In standard Life, that same collision produces an object with no memory of the fight. In Immigration, you can look at the wreckage and read off exactly which color contributed which cells.

Two extensions, one that worked and one that didn't

Immigration's two-color version stayed simple because three cells can't tie between two groups. Push to more colors and that stops being true — three parents could easily be three different colors, no majority at all. Two answers to that problem came out of the same LifeLine era, and only one of them held up.

Dean Hickerson's fix, 1973. Koenig again, describing what Hickerson presented in LifeLine #11:

"The majority rule is again applied, but in this case, when three different states were involved in a birth, the fourth state results instead."

Call it 5-State Life (four colors plus "off") or, in the name it goes by in modern implementations like Golly, QuadLife: with four colors, a birth either has a clear 2-1 majority (that color wins, same as Immigration) or a three-way tie among different colors (the fourth, uninvolved color wins instead). It's a genuinely elegant patch — every birth still resolves deterministically, no coin flips, no external state.

Gunnar Johnsson's fix, contemporaneous. Instead of picking a discrete winner, Johnsson's "Rainbow Game of Life" (also described in Koenig's retrospective) took the arithmetic mean, in RGB space, of the three parents' colors. It sounds more expressive — infinite shades instead of four — but Koenig's verdict on why it doesn't actually work is blunt: "after a while, most active patterns will settle down to a muddled gray." Averaging colors has no way to reintroduce a saturated color once it's been diluted; the game visually flattens into noise. QuadLife's discrete four-way rule keeps every birth crisp specifically because it refuses to blend.

The lesson generalizes: the reason Immigration and QuadLife still get implemented fifty-plus years later, and Rainbow Life is a historical footnote, is that averaging destroys the one thing color was tracking — which side actually won a given fight. A rule that blends inputs together can't keep score. A rule that picks a winner can.

The competitive spark nobody picked up for thirty years

Here's the detail that made us want to write this up: Koenig's account of Woods' original 1971 proposal doesn't stop at coloring. In parentheses, almost as an aside:

"The game, called Immigration, also had players adding bits in order to influence the outcome of births, which violates Life's determinism, but does add a competitive element."

Two actual players, each nudging the board to swing majorities their way — that's a real competitive game, sketched out in 1971, two years before LifeLine even finished its run. And then, as far as the record shows, nobody built on that half of the idea for decades. Martin Gardner's 1983 verdict that competitive Life attempts had produced "no memorable results" came twelve years after Immigration's core mechanic already existed with competitive intent attached. The academic paper that finally took the challenge seriously — p2life, 2002 — rediscovered Immigration's majority-birth rule as its starting point and explicitly built survival competition on top of it. The implementations that actually shipped since then, lifecompetes.com among them, converged on the same majority-color ownership rule Woods described, plus a resource economy to make placing cells matter.

We wrote up that whole hunt separately. What's worth sitting with here is how early the real idea showed up, and how long the "add competition" half of it sat untouched while everyone else treated Life as strictly zero-player.

Why we're building on this specific rule

Every shipped multiplayer Life implementation we could verify uses Immigration's majority-color birth rule as its ownership mechanic, and it's the rule we're designing our own turn-based duel around: two players, a shared board, births resolved by majority color exactly as Woods described, with a limited per-turn cell budget as the resource that actually makes it a game rather than a simulation. It's not live yet — but if the fifty-year track record of this one rule is any indication, it's the right foundation to build on rather than invent around.

In the meantime, the mechanic is simple enough to check by hand. Take any two-color collision, count the parents on each birth, and you've already played a round of a fifty-five-year-old rule. Or skip the bookkeeping: our pattern library has the gliders and oscillators to collide, our simulator will run them, and our MCP server — walked through step by step here — can step any pattern forward exact generations and check a predicted outcome against the real thing, useful for verifying collision results without doing the neighbor-counting by hand, color-tracking included, one collision at a time.