Emergence · Behavioral Taxonomy

Pattern Field Guide

Sixteen behavioral archetypes observed in particle life. Each arises from specific matrix conditions — none are scripted. This guide describes what to look for, what produces it, and how the real-time detector identifies it.

16 patterns · 4 classic · 12 newly identified


Classic patterns

The four foundational archetypes

These were the first behavioral classes identified in particle life systems. They appear consistently across different implementations and have been informally described in the literature since Ventrella's Clusters (1994).

🔬 01 Common

Membrane

A dense, near-stationary cluster of one species that holds its shape and resists dispersion. The simplest stable structure — particles find a potential minimum and stay there, vibrating slightly but never escaping. Looks like a living cell under a microscope when a second species forms around it.

The membrane is the most frequent and most foundational pattern. It appears in a wide range of matrices — anywhere a species strongly self-attracts or is attracted to a stationary target species. Most complex patterns (rings, proto-cells, vortices) require a membrane-like core to nucleate around.

Detection signature
  • Speed < 0.035 — cluster is nearly stationary
  • Cohesion < rMax × 1.5 — particles are tightly packed
  • Hollowness < 0.30 — no empty interior
  • Aspect ratio < 2.5 — roughly compact/circular shape
Matrix conditions: Species A self-attracts strongly (diagonal value > 0.6). OR species A attracts B, B weakly repels A — creating a shell of A around a stationary B core.
🎯 02 Uncommon

Chase Sequence

A compact cluster moves across the field with directed velocity, closing on another cluster. On contact, the target cluster disperses or reforms elsewhere. The chaser reassembles and hunts again. From the outside it looks exactly like predation — but the chaser has no awareness of its prey and no memory of prior hunts.

What the detector identifies is kinematic: the chaser's center-of-mass velocity is aligned with the direction toward the prey cluster. There is no representation of intent anywhere in the code.

Detection signature
  • Two clusters identified from different species
  • Dot product of A's velocity and (B.pos − A.pos) > 0.72
  • This alignment must persist across multiple frames
  • A is moving toward B faster than random drift
Matrix conditions: A strongly attracts B, B repels A. A self-attracts (keeping tight). This asymmetry is the engine: B's fleeing creates a persistent gradient that A follows.
🌬️ 03 Uncommon

Breathing

A cluster's radius oscillates — expanding and contracting rhythmically. The period is not set by any clock. It emerges from the force balance: mutual attraction pulls particles inward, inertia carries them past equilibrium, the core's repulsion pushes them back out. A standing wave in configuration space.

The detector measures the mean distance from centroid over a rolling window, flags a breathing event when the amplitude exceeds a threshold, and applies a cooldown to prevent repeated triggers on the same oscillation.

Detection signature
  • Centroid tracked over rolling buffer (not from origin — centroid)
  • Mean distance from centroid oscillates with amplitude > threshold
  • Cluster cohesion alternates between tight → loose → tight
  • Periodicity confirmed across at least two full cycles
Matrix conditions: Near-symmetric mutual attraction between two species (A↔B ≈ equal and positive). High enough damping to prevent escape; low enough to allow the overshoot that creates oscillation.
🌌 04 Uncommon

Galaxy

A rotating structure with a dense core and trailing spiral arms. The rotation isn't programmed — it's a consequence of angular momentum transferred during the asymmetric collapse of a forming cluster. As new particles fall in from off-axis trajectories, they contribute torque; the whole structure begins spinning and holds its spin through conservation.

Galaxies grow over time, absorbing nearby loose clusters into their arms. Given a large enough field, a single galaxy can eventually incorporate most of the particles of its species.

Detection signature
  • Large cluster (top percentile by size)
  • Net angular momentum > 0 (persistent spin direction)
  • Aspect ratio near circular — spiral arms are dynamic, not static elongation
  • Large reach parameter amplifies the gravity-like collapse
Matrix conditions: One species has strong self-attraction. Large rMax (reach) creates long-range gravitational-like pull. Moderate cross-species attraction supplies angular momentum during formation.

Newly identified patterns

Twelve new archetypes

These twelve behavioral classes were identified through systematic exploration during the development of Emergence. They have not, to my knowledge, been formally named or computationally detected in prior particle life implementations. Each has a detector with measurable geometric criteria running in real time.

05 Uncommon New

Ring Structure

A hollow annulus of particles: particles are arranged in a closed loop with an empty center. The ring is structurally stable — it holds its shape against perturbation and drifts as a unit. Unlike the membrane (which is a solid disc), a ring has a measurable void at its center.

Rings are what happens when the repulsive core is strong enough to push particles away from a central nucleus while the interaction band creates just enough cohesion to keep them looping around it. The geometry is not designed — it's the only stable orbit at that force balance.

Detection signature
  • Hollowness score > 0.48 — significant empty interior
  • Cluster size > 14 particles — enough to form a closed loop
  • Aspect ratio < 2.2 — ring is circular, not an arc
Hollowness metric
  • Grid centroid located from particle positions
  • Empty cells in inner 40% of bounding circle counted
  • Score = empty_inner / total_inner — higher = more hollow
Matrix conditions: Strong self-repulsion prevents collapse; weak self-attraction maintains cohesion. OR: species A is attracted to species B at medium distance, while B is positioned at the ring center. A orbits B without reaching it.
🧫 06 Rare New

Proto-Cell

A ring membrane of one species enclosing a different species in its interior. This two-layer structure — an inner core of species A, surrounded by a hollow ring of species B — is the closest analog to a biological cell yet observed in particle life.

Unlike a plain membrane (which may just be a shell of one species), the proto-cell requires that the interior contains a measurable cluster of a different species within the ring's radius. Both components must be stable simultaneously. This is genuinely difficult to achieve and represents a higher-order emergent structure.

Detection signature
  • A ring structure is detected (hollowness > 0.48)
  • A separate cluster of a different species found near ring's centroid
  • Interior cluster's centroid is within ring.cohesion × 0.6 of ring center
  • Both structures stable simultaneously for ≥ 2 detection frames
Matrix conditions: A (interior) and B (ring) must have asymmetric interaction: B strongly attracts A at medium range, A mildly repels B (keeping the ring from collapsing inward). B must also have enough self-cohesion to maintain its ring shape.
🌀 07 Rare New

Vortex

A cluster with significant net angular momentum — particles are not just circling loosely but collectively rotating in a consistent direction, producing a visual spiral or swirl. The rotation direction (clockwise or counterclockwise) is arbitrary and determined by the initial particle positions; it persists for as long as the matrix supports the vortex.

Vortices sit at a fascinating point: they have net angular momentum but no mechanism enforcing conservation — nothing is preventing angular momentum from dissipating through damping. That they persist means the force geometry actively reinforces the rotation rather than merely tolerating it.

Detection signature
  • |Angular momentum| > rMax × 0.025
  • Hollowness > 0.30 — some interior space (not a solid clump)
  • Cluster size > 12 particles
  • Angular momentum = Σ (r × v) per particle, summed and divided by N
Matrix conditions: Cyclic dominance or asymmetric multi-species interaction creates a persistent force asymmetry that drives rotation. The Spiral preset (A→B→C→A cyclic attraction) reliably produces vortices.
🧵 08 Uncommon New

Filament

An elongated thread or chain of particles — particles strung in a line, like a polymer or a muscle fiber. Where membranes form compact discs and rings form circles, filaments form extended linear structures with high aspect ratio.

The emergence of filaments hints at the physics of polymer formation: particles find a stable one-dimensional configuration when the force curve penalizes broad clustering but rewards tight pairwise bonding. Chain-forming conditions are sensitive — most matrices that produce chains also produce membranes or vortices, and the transition between regimes is sharp.

Detection signature
  • Aspect ratio > 3.2 — significantly elongated
  • Cluster size > 10 particles
  • Aspect ratio = max principal component / min principal component (PCA of particle positions)
Matrix conditions: A attracts A at precisely medium range (interaction band peak only), combined with a narrow repulsive core. This creates bead-string geometry: particles can't collapse together but can't spread apart either. Low rMax (reach) also encourages linear over planar packing.
🛸 09 Very Rare New

Glider

A small, compact, coherent structure that self-propels across the field. Unlike a chaser (which follows another cluster) or a swarm (which is a moving loose group), a glider moves without an external target — it maintains its shape and velocity as a self-sustaining kinematic object.

Gliders are the rarest pattern in the simulation — comparable to the glider in Conway's Game of Life in rarity and significance. They represent a genuinely surprising property: a configuration of interacting particles that acts as a stable moving object, propagating itself through space by its own force dynamics. Finding one manually can take hours of exploration.

Detection signature
  • Speed > 0.04 — moving consistently
  • Cohesion < rMax × 1.1 — very tight cluster
  • Hollowness < 0.30 — solid, not a ring
  • Aspect ratio < 2.5 — compact shape
  • Small size (few particles) — gliders are small by nature
  • No target cluster within range (not a chaser)
Matrix conditions: Extremely sensitive to parameters. Cross-species forces must create an asymmetric propulsive geometry: one species acts as a "fuel" that the glider consumes (reconfigures) as it passes through. Most common near cyclic or near-antisymmetric matrices. Use the Evolve button to search for them — random exploration is very unlikely to find a glider within a few presses of R.
🪐 10 Rare New

Binary Orbit

Two clusters in mutual orbit — circling each other like a binary star system. The relative velocity of the two clusters is predominantly perpendicular to their separation vector, meaning they are continuously "missing" each other as they rotate around a shared center of mass.

Binary orbits are rare because they require a specific balance: strong enough mutual attraction to maintain the bond but weak enough to not cause the clusters to merge. They also require low enough damping that kinetic energy isn't bled off before the orbit stabilizes.

Detection signature
  • Two clusters identified
  • Cross-product |vrel × r̂| > 0.015 (significant perpendicular motion)
  • Cross-product > along-product × 1.4 (orbit, not approach)
  • Angular rate = cross / (dist + ε) — orbit frequency computed
Matrix conditions: A and B mutually attract at medium-to-strong strength (M[A][B] and M[B][A] both positive and similar). Low damping. Medium rMax. Initial positions must give some angular momentum; identical symmetric attraction would just cause them to merge.
🎨 11 Common New

Phase Separation

Species spontaneously segregate into macroscale territories — each color claiming its own region of the field with sharp boundaries between them. Starting from uniform mixing, the simulation self-organizes into a spatial map. The boundaries are dynamic (they move and shift as clusters grow or shrink) but the separation itself is self-sustaining.

This is the particle life analogue of oil-and-water phase separation in thermodynamics — a collective phenomenon that requires no individual particle to "know" about the global structure. Each particle just follows local forces, and the global pattern is an inevitable consequence.

Detection signature
  • Field divided into a grid; species distribution per cell measured
  • Entropy of species distribution per cell is low (each cell dominated by one species)
  • Global entropy averaged across grid; separation fires when well below expected for uniform mixing
  • Requires numTypes ≥ 3 — not meaningful with 1–2 species
Matrix conditions: Each species self-attracts more strongly than it cross-attracts (diagonal values dominate). Mutual repulsion between species accelerates separation but isn't required — even neutral cross-interactions produce separation given strong enough self-attraction.
🌙 12 Uncommon New

Arc Crescent

A curved open structure — a partial ring that does not close. Where a ring is a closed loop with a hollow center, an arc is a crescent or parenthesis shape: curved, but open at both ends. The arc occupies an intermediate zone between a compact membrane and a full ring, caught at the moment where curvature exceeds width but closure has not yet occurred.

Arcs are remarkably common in energetic or high-reach fields where ring formation is interrupted by collisions or shear. A ring that loses particles from one side becomes an arc; a membrane elongating under anisotropic forces curves into one. The open ends do not collapse — they are held apart by the same internal stresses that produced the curvature.

Detection signature
  • Aspect ratio 1.8 – 3.2 — more elongated than a disc, less than a filament
  • Hollowness 0.22 – 0.48 — concave interior, but not a closed ring
  • Cluster size > 10 particles
  • Catches the crescent zone between membrane (compact) and ring (fully hollow)
Matrix conditions: Intermediate between ring and membrane — a species self-attracting with moderate force and a repulsive core strong enough to prevent collapse but not quite sufficient to sustain a closed ring. A partially asymmetric matrix or cross-species shear tends to curve membranes into arcs.
🐝 13 Uncommon New

Swarm

A compact, coherent group of particles that moves as a unit at high velocity. Unlike a membrane (nearly stationary) or a glider (very small and self-propelling), a swarm is large — a significant fraction of all particles of its species — and moves because the local force geometry gives the entire group a net drift direction that each individual particle sustains.

The swarm's coherence is purely emergent: no particle knows about the group. Each responds only to its immediate neighbors. But because velocity fields of tightly packed particles in the interaction zone are correlated, the group acquires a shared drift. The visual effect is reminiscent of murmuration — coordinated mass motion from purely local rules.

Detection signature
  • Speed > 0.08 — fast group motion
  • Cohesion < rMax × 1.3 — particles remain close
  • Hollowness < 0.35 — solid group, not a ring
  • Size > max(8, N × 0.04) — large enough to be a true group
Matrix conditions: The species self-attracts moderately, keeping the group together, while also attracted to a second species that is itself moving. The cross-species attraction provides a drag force in the direction of the target species; the self-cohesion prevents the swarm from dispersing in its own wake.
🚀 14 Rare New

Mobile Cell

A proto-cell — a ring membrane enclosing an interior cluster of a different species — that has acquired net translational velocity. The entire two-layer structure moves together through the field without losing structural integrity. The motion is not driven by an external attractor; the cell is self-propelling due to a slight internal force asymmetry that was frozen in during formation.

The mobile cell is the most complex stable object regularly produced in particle life. It encodes information (the species combination and ratio) in a structure that persists through both space and time. Its existence is what prompted calling the static version a "proto-cell" — a cell, by biological definition, moves.

Detection signature
  • A proto-cell is detected — ring cluster enclosing a different-species interior cluster
  • Ring's center-of-mass speed > 0.03 — the whole structure is in motion
  • Interior cluster moves with the ring (not left behind)
  • Structure must hold together across at least 2 detection frames
Matrix conditions: Same as proto-cell, but with a slight additional asymmetry in the cross-species matrix or a momentum imbalance inherited from the formation trajectory. Low damping helps: the cell retains its formation velocity rather than settling to rest.
🎡 15 Very Rare New

Mosaic Ring

Three or more distinct species arrange themselves into adjacent arc segments that collectively form a complete ring around a shared empty center. Each species holds one portion of the circumference, and the segments are stable neighbors — the boundary forces between species are balanced precisely enough that no segment expands to consume the others.

The mosaic ring is perhaps the most striking visual in particle life: a multi-colored ring assembled spontaneously from particles that have no awareness of the overall shape. It requires multiple species to simultaneously find a mutually compatible spatial arrangement — a combinatorial rarity that makes the mosaic ring exceptional whenever it occurs.

Detection signature
  • 3+ distinct species clusters in close proximity (within rMax × 3.5)
  • All clusters arranged at consistent radius from a shared centroid (low radial variance)
  • Largest angular gap between any two adjacent clusters < 180°
  • All participating species clusters detected simultaneously
Matrix conditions: Each species must self-attract enough to maintain its arc, while being mildly attracted to (or compatible with) its ring-neighbors. Too strong cross-species repulsion destroys the ring; too strong cross-species attraction causes merging. The balanced zone is narrow.
〰️ 16 Rare New

Helix

An elongated structure whose particles are arranged in a wave or sinusoidal pattern rather than a straight line. Looking perpendicular to the major axis, particles cluster at ±offset from center — the cross-section is bimodal rather than unimodal. In three dimensions this would be a helix; in this 2D projection it appears as a sinusoidal wave chain.

The helix is a transient structure that often precedes more stable configurations. As a helical chain winds tighter, angular momentum accumulates in one direction — the helix may eventually collapse into a vortex or a galaxy. Observing the helix → galaxy transition is rare and captures a dynamical process that has no obvious analog at the level of individual particle rules.

Detection signature
  • Aspect ratio > 3.5 — highly elongated (stricter than filament)
  • Hollowness < 0.42 — not a closed ring
  • Cluster size > 14 particles
  • Minor-axis projection is bimodal: outer thirds hold more particles than the center third
  • Each outer third > 18% of total; center third < 55% of outer sum
Matrix conditions: Similar to filament, but with a slight repulsive interaction between same-species particles at very short range. This prevents simple linear packing and forces a wave geometry. Low damping preserves the sinusoidal oscillation rather than letting it decay into a straight chain.

How detection works

The pattern classifier

All sixteen detectors run simultaneously in the simulation, throttled to every 6 frames with per-pattern cooldowns to avoid event spam. Here is the shared infrastructure behind every detection.

BFS Cluster Finder

Every detection pass begins with a spatial BFS (breadth-first search) that groups nearby same-species particles into clusters. Particles within rMax of each other are connected. The algorithm runs in O(N) time using the same spatial hash grid as the physics engine.

Each cluster is then annotated with geometry: centroid, mean speed, mean distance from centroid (cohesion), hollowness score, aspect ratio (PCA), and angular momentum. These five metrics feed every downstream classifier.

Per-cluster metrics
  • speed — mean center-of-mass velocity magnitude
  • cohesion — mean distance of particles from cluster centroid
  • hollowness — fraction of inner bounding area that is empty
  • aspect ratio — principal component ratio (PCA on positions)
  • angular momentum — Σ(r × v) / N about centroid
Detector thresholds (summary)
  • Membrane — speed<0.035, cohesion<1.5r, hollow<0.30, AR<2.5
  • Ring — hollow>0.48, size>14, AR<2.2
  • Proto-Cell — ring + inner cluster of different species
  • Vortex — |L|>0.025r, hollow>0.30, size>12
  • Arc — AR 1.8–3.2, hollow 0.22–0.48, size>10
  • Filament — AR>3.2, size>10
  • Helix — AR>3.5, bimodal minor-axis projection
  • Glider — speed>0.04, cohesion<1.1r, hollow<0.30, AR<2.5
  • Swarm — speed>0.08, cohesion<1.3r, hollow<0.35, large size
  • Chase — v̂·r̂ > 0.72 (velocity aligned to target)
  • Orbit — cross(v_rel, r̂)>along × 1.4
  • Galaxy — vortex with slow dense core enclosed inside
  • Mobile Cell — proto-cell with speed>0.03
  • Mosaic Ring — 3+ species clustered in ring with gap<180°
  • Phase Sep. — per-cell entropy below uniform baseline

Found something?

Seen a pattern that isn't named here?

These sixteen archetypes are what I've found so far — but particle life's state space is enormous. There are certainly configurations that produce structures I haven't seen yet. If you find something strange, something beautiful, or something that doesn't fit any of these categories, I genuinely want to know.