Seeds: Pure Birth, No Memory
Seeds is the only cellular automaton in which nothing ever survives — and it generates some of the most explosive growth patterns in rule space.
That is the paradox at the center of B2/S. Remove survival entirely — every live cell dies every generation, no exceptions — and you might expect the rule to be inert. Instead, Seeds produces rapidly expanding waves that fill a grid within a few hundred generations, supports structures that function as spaceships and rakes, and generates churning, complex interior activity with no stable element anywhere. A rule incapable of preserving a single cell turns out to be capable of sustained, structured propagation on a large scale.
The mechanism is birth. In Seeds, a dead cell with exactly 2 live neighbors is born. The live cells that trigger that birth are themselves dead one tick later — but by then, the newly born cells are triggering further births. The rule has no memory and no persistence, only a chain of births cascading forward from the initial seed. The name is exact: each generation casts the seeds of the next, which cast the seeds of the one after, with nothing ever carrying forward.
The Rule: B2/S
Seeds is written B2/S, the simplest possible way to write a rule with an empty survival set:
- A dead cell is born if it has exactly 2 live neighbors.
- A live cell always dies, regardless of its neighbor count.
The simplicity of this description conceals how unusual the rule is. Every other Life-like rule with interesting behavior has some cells that survive from one generation to the next. Survival is how patterns accumulate structure — still lifes exist because cells survive, oscillators exist because cells take turns surviving, spaceships exist because a moving wave of cells collectively maintains its shape through alternating death and birth.
Seeds strips survival out entirely. The rule is named for the image of a pattern as a seed: each generation casts the seeds of the next, which cast the seeds of the one after that, with nothing ever carrying forward.
Brian Silverman, the computer scientist who also devised Brian’s Brain, initially investigated Seeds. The name was given to the rule by Mirek Wójtowicz, whose Cellular Automata rules lexicon helped systematize and name many Life-like rules in the 1990s and 2000s.
Why B2/S Is the Extreme Case
To understand what Seeds reveals, it helps to think about where it sits in the space of all Life-like rules.
Consider a dial that controls the “birth aggressiveness” of a rule — how easily dead cells become alive. At one extreme, B0 (birth with zero neighbors) causes the entire empty grid to fill instantly. At the other, empty B (no birth conditions at all) means nothing is ever born. Seeds uses B2 — a moderate birth condition, requiring exactly 2 neighbors for birth — but combines it with the most extreme possible survival condition: S (empty), meaning no cell ever survives.
This combination — moderate birth, zero survival — creates a pure reaction without inhibition. Every live cell that is born on tick n is dead by tick n+1. The “population” of live cells at any moment is entirely made up of freshly born cells. They have no history. They carry no state forward.
Contrast this with Conway’s Life, which balances birth-at-3 with survival-at-2-or-3. In Life, cells accumulate: stable structures persist for generations, oscillators maintain their state across many ticks, computation is possible because information can be stored in long-lived patterns. In Seeds, nothing accumulates. Every tick is the grid’s first tick, so to speak — the only history that matters is the set of live cells one step ago, which are all about to die.
Dynamics: Explosive Propagation
Despite its simplicity, Seeds produces visually striking behavior.
Start with almost any finite pattern — even a single pair of adjacent cells — and it will rapidly expand into a growing, roughly circular blob of activity. The blob grows at approximately the speed of light (one cell per generation in each direction), and it does not have a stable interior: the inside of the blob churns constantly, with new cells being born and dying in complex patterns that depend on the initial seed.
The birth condition — exactly 2 live neighbors — determines which configurations actually trigger births. A single isolated live cell produces nothing: the surrounding dead cells each have only 1 live neighbor, below the threshold. Two live cells placed directly adjacent to each other also produce no births: each has only 1 live neighbor (the other), so the dead cells surrounding the pair still fail the condition. Now consider two live cells separated by a single dead cell. That dead cell in the middle has exactly 2 live neighbors — one on each side — so it is born. The two flanking live cells die in the same tick, but the newly born center cell is now live, and by its position it grants exactly 2 live neighbors to further dead cells adjacent to it. The cascade propagates outward from there.
The expansion is not isotropic. Depending on the initial pattern’s geometry, the expanding wavefront develops characteristic structures: diagonal bands, corners, and sometimes surprisingly regular patterns that persist at the edges of the expanding region.
The Absence of Stability
Because no cell ever survives, Seeds has no still lifes by definition. A still life requires at least one cell that remains alive from one generation to the next, which is categorically impossible in B2/S.
Similarly, Seeds has no traditional oscillators — a period-n oscillator requires some cells to be alive at generation 0 and again at generation n, which requires survival.
What Seeds does have are 2-cycles: patterns that, after two generations, have returned to their original state. Since every cell alive at generation 0 is dead at generation 1, a 2-cycle must have the property that its generation-1 state (entirely new cells) produces, via births, the original pattern at generation 2.
These are the nearest analog to oscillators in Seeds, and they are genuinely remarkable: a set of cells that, while dying, cast births that exactly reproduce the original set. Finding 2-cycles in Seeds requires the pattern to be its own second-generation descendant — a strong self-referential constraint.
More complex analogs exist: 4-cycles, rakes (spaceships that emit other spaceships), and puffers (spaceships that leave trails behind). These exist in Seeds despite the absence of survival, because the birth-propagation mechanism is powerful enough to maintain certain pattern structures across many generations of pure birth dynamics.
Propagating Patterns
Despite — or because of — the constraint that nothing survives, Seeds supports a rich family of propagating structures.
The most common type is the diagonal wave: a structure that moves diagonally across the grid at speed c (one cell per generation diagonally), leaving behind an expanding region of chaotic birth-death activity. These diagonal waves arise naturally from almost any initial configuration and dominate the long-run appearance of Seeds.
Rakes (spaceships that emit other spaceships) have been found in Seeds. A well-known example is a period-4 rake discovered by Mirek Wójtowicz, which translates diagonally while periodically emitting smaller diagonal waves behind it. Its construction is remarkable given the no-survival constraint: the rake must maintain its own shape purely through birth dynamics, while simultaneously emitting additional birth-waves in a regular pattern. Puffers — spaceships that leave a permanent trail of debris rather than clean-emitting secondary ships — have also been catalogued. That these structures exist at all says something about how much organization birth-only dynamics can support. For a broader survey of how Seeds produces analogs to classical spaceship families — despite the total absence of survival — see Spaceships →.
When two expanding Seeds regions collide, the interaction is typically violent: the two expanding fronts interfere, creating complex interference patterns that may produce new propagating structures or simply reduce to chaotic expansion. Unlike Conway’s Life, where collisions can produce carefully engineered outcomes (eaters that destroy gliders, guns that emit them), Seeds collisions are almost impossible to engineer precisely — there is no stable “product” because nothing survives long enough to count as stable.
What Seeds Reveals About the Role of Survival
Seeds is not merely an exotic corner case. It is a controlled experiment in what birth alone can do, and by contrast, it reveals exactly what survival contributes to Life-like systems.
Survival enables information storage. In Conway’s Life, a block (a 2×2 square of live cells) persists indefinitely. It stores the fact that it was created. Subsequent patterns can interact with it and produce outputs that depend on its presence. This is the basis of computation in Life: persistent structures store state; gliders and other signals interact with those structures to process state. In Seeds, no pattern can store information longer than one generation. Seeds is computationally sterile — not in the sense that it produces no complex behavior, but in the sense that the complex behavior cannot accumulate into computation.
Survival enables stable objects. The entire taxonomy of Life objects — still lifes, oscillators, spaceships, guns, puffers — depends on cells surviving from one tick to the next. Seeds has none of this in the traditional sense. Its “objects” are better described as propagating fronts or periodic waves than as individual entities with boundaries and identities.
Survival enables localization. Patterns in Conway’s Life can be local: a glider occupies a small region of the grid and moves without affecting distant regions. In Seeds, almost everything eventually expands to fill the grid. Localized patterns are exceptional. The default behavior is explosion.
The lesson is not that survival is necessary for interesting behavior — Seeds clearly has interesting behavior, even complex behavior. The lesson is that survival and birth contribute categorically different things. Birth without survival produces richness that is diffuse, expansive, and amnesiac. Birth with survival produces richness that is local, persistent, and capable of accumulating structure.
Conway’s Life balances the two. Seeds shows what happens when balance is abandoned entirely in one direction. The other extreme — birth with total survival (Life Without Death, B3/S012345678) — shows what happens in the other direction: patterns grow without bound, never simplifying, filling the grid permanently. Both extremes are interesting. Neither is as interesting as the balance.