HighLife: A Replicator in the Wild
In 1994, Nathan Thompson was exploring the space of Life-like rules — the 262,144 possible two-state cellular automata that share Conway’s basic structure — when he tried adding a single birth condition to Conway’s rules. Instead of B3/S23, he used B36/S23: everything the same, except that a dead cell can also be born when it has exactly 6 live neighbors.
The two rules look nearly identical in practice. Run HighLife on the same starting configurations as Conway’s Life and you will mostly see the same things: gliders, blinkers, blocks, beehives. The familiar taxonomy of Life objects persists. The overall texture of the universe — sparse, complex, chaotic-but-organized — is the same.
And then, sometimes, you see something that doesn’t exist in Conway’s Life at all. A pattern begins to copy itself. Not approximately. Not metaphorically. Exactly: an identical pattern appearing at a fixed displacement, every 12 generations, without any external mechanism to make it happen. Self-replication, arising spontaneously from a one-digit change to a rule.
This is the HighLife replicator, and it is the reason HighLife is by far the most studied Conway variant.
The Rule: B36/S23
HighLife is defined by the rule B36/S23:
- A dead cell is born if it has exactly 3 or 6 live neighbors.
- A live cell survives if it has exactly 2 or 3 live neighbors.
- All other live cells die; all other dead cells stay dead.
The survival rule (S23) is identical to Conway’s Life. The birth rule adds exactly one entry: 6. A dead cell surrounded by 6 of its 8 neighbors becomes alive in HighLife; in Conway’s Life, that cell would stay dead.
The consequence of this single addition is almost entirely invisible in ordinary play. The most common patterns — blocks, blinkers, beehives, boats, gliders, the standard spaceships — all behave identically in HighLife and Conway’s Life. The reason is that these patterns are sparse: the cells involved rarely accumulate six live neighbors. Adding birth-at-6 to the rule makes no difference unless a cell actually has six neighbors, which in sparse configurations almost never happens.
The replicator is an exception. It is a pattern in which six-neighbor configurations arise precisely at the right places, in the right sequence, to trigger replication. The birth-at-6 rule is the mechanism that makes it possible.
The Replicator
Thompson’s replicator is a compact, symmetric pattern. In its standard form it consists of approximately 22 live cells arranged in a roughly symmetric cluster. It is small enough to occur spontaneously from random initial configurations — which makes it unusual even among replicators.
What it does
After exactly 12 generations, the replicator has produced an identical copy of itself displaced 4 cells diagonally (2 cells in one direction, 2 in the perpendicular). The original pattern is intact at its original location. The copy is intact at the displaced location. Two replicators now exist where one existed before.
After another 12 generations (24 total), each of the two replicators has produced a copy. Four replicators now exist, spread along a diagonal line.
After another 24 generations (48 total), eight replicators. Then sixteen. The count doubles at every doubling interval. More precisely: at generation 12(2ⁿ − 1), there are 2ⁿ copies of the replicator, spaced 4 cells apart along the diagonal.
The two ends of this growing line of replicators expand at speed c/6 — that is, one cell diagonally every 6 generations, where c is the maximum information-propagation speed in the grid. The replicator line is itself a kind of spaceship, though one that grows rather than simply moving.
The bomber: a replicator turned spaceship
Nathan Thompson also discovered what is now called the bomber: a pattern consisting of a replicator and a blinker in specific relative positions. Here’s what happens: the replicator duplicates itself, producing two replicators. One of the two new replicators interacts with the blinker — and that interaction “kills” the old replicator while pulling the blinker forward to a new position matching the surviving replicator. The whole configuration — one replicator, one blinker — has shifted by 2 cells diagonally, and it will do the same thing again next period. The period is 48 generations. The bomber travels at speed c/6 diagonally and is a genuine spaceship built from a replicator and an oscillator.
Why Birth-at-6 Enables Replication
The reason adding 6 to the birth list enables self-replication is not simple, but the intuition is worth tracing.
In Conway’s Life, the birth rule (3 neighbors) and survival rule (2 or 3 neighbors) were chosen partly to prevent explosive growth: cells need just enough support to be born and survive, but too much crowding kills them. Six is a high neighbor count — a dead cell surrounded by 6 live neighbors is deeply embedded in a dense region. Under Conway’s rules, such a cell stays dead. Under HighLife’s rules, it is born.
The replicator works by creating, through its internal evolution, exactly such dense regions at specific locations ahead of its “direction of travel.” The birth-at-6 rule fires in precisely those locations, creating new cells that go on to form the second copy. Meanwhile, the original pattern’s internal dynamics continue to maintain the original pattern. The two processes — maintaining the original, creating the copy — don’t interfere because the geometry works out exactly right at 12-generation periods.
This is not an accident. Thompson found the replicator by searching for it — looking for patterns in HighLife that the birth-at-6 condition made possible. But the pattern’s existence is not arbitrary: it reflects a genuine structural property of the B36/S23 rule. Given that rule, a sufficiently small and well-structured pattern can exploit the six-neighbor birth condition to copy itself.
Self-Replication Without Turing Completeness
Here is the most important non-obvious fact about the HighLife replicator: it demonstrates that self-replication does not require Turing completeness or universal construction.
John von Neumann, in the 1940s, proved that a self-replicating automaton must contain a universal constructor — a machine capable of building any pattern given a description of that pattern. His self-replicating design had 29 cell states and was enormously complex. The implicit message was that self-replication is hard: it requires a machine that can, in principle, construct anything.
Conway built his rules partly in response to von Neumann’s challenge, looking for something simpler that might still support computation and possibly replication.
The HighLife replicator bypasses von Neumann’s logic entirely. It doesn’t construct a copy by reading a blueprint and assembling components. It replicates the way a crystal replicates: by creating local conditions that force the substrate to organize into the same structure. There is no general constructor. There is no blueprint. The pattern simply has the property that its evolution, under these specific rules, produces a geometric copy.
This form of replication — sometimes called template replication or physical replication — is structurally much simpler than von Neumann’s constructive replication. It does not require the replicator to be able to build arbitrary patterns. It only requires the pattern to be stable and geometrically self-reinforcing under the rule.
The implication is significant: self-replication in complex systems is not necessarily a sign of high organizational sophistication. It can arise from quite modest local interactions, given the right rule. The difficulty of self-replication in Conway’s Life is not an intrinsic property of self-replication — it is a property of Conway’s specific rules. HighLife shows that one birth condition away from Life, self-replication becomes almost easy.
Comparison with Engineered Self-Replication in Life
Conway’s Life does support self-replication — but not a natural one. In 2010, after decades of work, the Life community produced a self-replicating pattern: a configuration capable of reading a “tape” encoded as a stream of gliders and constructing a copy of itself. The pattern was enormous — hundreds of thousands of cells in its working parts — and required years of engineering by many contributors.
The HighLife replicator is 22 cells. It occurs spontaneously from random soup. These two numbers tell the story.
The contrast is not a criticism of the Life community’s achievement — the Life self-replicator is a stunning piece of engineering, and it does something the HighLife replicator cannot: because it is a genuine universal constructor, it can in principle build any pattern, not just copies of itself. It is a machine. The HighLife replicator is a crystal.
What the contrast reveals is that there are at least two fundamentally different mechanisms by which a pattern can replicate, and they require very different computational sophistication. Template replication (HighLife) is a local geometric property. Constructive replication (Life, von Neumann) is a general computational capability. The latter implies the former; the former does not imply the latter.
Other Properties of HighLife
Beyond the replicator, HighLife is rich in its own right.
The standard Life objects — blocks, boats, beehives, blinkers, toads, beacons, gliders, LWSSs, MWSSs, HWSSs — all survive unchanged. HighLife can run anything Life can run in sparse configurations. It is in this sense a proper extension of Life: everything Life can do, HighLife can do, plus more.
HighLife additionally supports the bomber spaceship (c/6 diagonal) that Life does not have, and a range of other patterns that exploit birth-at-6 in less dramatic ways.
Whether HighLife is Turing-complete in the same sense as Conway’s Life has not been definitively established — the typical route to Turing-completeness in Life relies on glider guns and logic gates assembled from standard Life components, which all transfer to HighLife unchanged. Most researchers assume HighLife is at least as computationally capable as Conway’s Life, since it contains Life as a sub-system (at low densities where birth-at-6 never fires).
The deepest question HighLife raises is not computational. It is: if self-replication arises this easily from a minimal rule change, how common is it in the broader space of possible rules? Is HighLife exceptional, or is it evidence that natural replicators are surprisingly common once you leave the immediate neighborhood of Conway’s specific choice?
That question remains open. The handful of other rules with known natural replicators suggests they are genuinely rare — but not nearly as rare as the difficulty of engineering replication in Conway’s Life might suggest.