Primordia

A few kinds of particle, a table of who attracts and repels whom, and nothing else. Let it run. Cells form, membranes appear, things that look like organisms crawl and split and chase. Life, or a convincing rumor of it, out of a rule small enough to fit on an index card.

The concept

Give each particle a species, and define forces not by physics but by a matrix: species A is drawn to B, repelled by C, indifferent to D. Asymmetry is the secret, if A chases B but B flees A, you get motion that never settles. From that single table, with no notion of "cell" or "organism" anywhere in the code, structure self-assembles: clusters with skins, things that engulf, things that reproduce.

The math

Each particle feels a short-range force from its neighbours weighted by the interaction matrix $A_{s_i s_j}$ between their species:

$\mathbf{F}_i = \sum_{j \neq i} A_{s_i s_j}\, g\!\left(\lVert \mathbf{r}_j - \mathbf{r}_i \rVert\right)\, \hat{\mathbf{r}}_{ij}$

where $g$ is a finite-range profile (attraction in a mid band, hard repulsion up close so particles do not collapse). Velocities are damped each step, so the system is dissipative, not conservative, which is what lets it find and hold structure instead of flying apart. The whole zoo is controlled by the numbers in $A$.

Why it stays strange

There is no fitness function, no goal, no selection. The "lifelike" behaviour is not optimised for; it is simply what this particular matrix does, and a small change to one entry can switch a thriving ecosystem into static dust or boiling chaos. It is the cleanest demonstration that the line between "chemistry" and "life" might be far thinner, and far more about organisation, than it feels.

Further reading

• Langton (1986), "Studying Artificial Life with Cellular Automata."
• Schmickl et al., on particle-based artificial life ("Lenia" and kin).

@article{langton1986,
  author  = {Langton, Christopher G.},
  title   = {Studying Artificial Life with Cellular Automata},
  journal = {Physica D},
  volume  = {22},
  number  = {1--3},
  pages   = {120--149},
  year    = {1986}
}