Particle Life

Organisation before biology. Give particles almost nothing—a colour, a velocity and a directed table of attractions and repulsions—and asymmetric pair rules can still assemble clusters, rings and chase waves. The sphere asks how much morphology can appear when no particle carries a body plan or a goal.

The central mathematical object is a directed interaction matrix (A). If a particle of type (i) encounters a particle of type (j), the entry (A_{ij}) determines whether and how strongly (i) accelerates toward or away from (j). The reverse response is stored separately:

Compact form: A_ij ≠ A_ji

is allowed.

That inequality is the most important fact in the sphere. It makes the interactions nonreciprocal. Type A can be attracted to type B while B is repelled by A. One population then pursues while the other escapes, despite the absence of perception, intention or strategy. With three or more types, directed cycles of attraction and avoidance can create persistent chase fields and circulating structures.

Tom Mohr’s Particle Life documentation describes the matrix in exactly this directed form: when types (i) and (j) meet, the acceleration applied to (i) comes from matrix(i,j), while the acceleration applied to (j) comes independently from matrix(j,i). Jeffrey Ventrella describes Clusters, the acknowledged precursor, as an asymmetrical particle system and explicitly contrasts its relationship-like forces with particles obeying ordinary Newtonian action–reaction symmetry.

This establishes the first major distinction from Gravity. Gravity applies a common attractive principle associated with source mass. Particle Life gives each ordered pair of types its own rule. The world is therefore closer to a directed relationship network embedded in space than to a toy molecular dynamics simulation.

The interaction is finite-range. A particle responds only to neighbours within a maximum radius (R). In the current AL.Floys implementation, the matrix coefficient is transformed into an attraction or repulsion strength, multiplied by a distance-dependent falloff, and applied along the direction between the particles. A compact explanatory approximation is

Compact form: \Delta v_i \propto Σ_j:d_ij<R r̂_ij sgn(A_s_i s_j) |A_s_i s_j|^0.75 \left(1-\fracd_ijR\right)^q + short-range repulsion + turbulence.

This equation is a readable summary of the code, not a claim that all Particle Life implementations use the same force curve. AL.Floys adds separate attraction and repulsion boosts, a configurable force exponent, anti-collapse force at very short distance, velocity retention and a speed cap.

The radius changes more than graphical scale. It changes the interaction network. At any moment, particles inside the radius are connected by directed forces. A larger radius creates a denser, more globally connected network; a smaller radius breaks the world into local components. Large coherent structures can therefore disappear when the radius falls below the scale needed to maintain connectivity.

Nonreciprocity also makes the system fundamentally nonequilibrium. In ordinary isolated mechanics, reciprocal pair forces and conservation laws constrain what persistent motion can occur. Here, matrix asymmetry can produce net directed pair motion; damping continually removes velocity; turbulence injects perturbations; the speed cap truncates extreme responses. The simulation is an explicitly driven and dissipative artificial world rather than a conservative physical system.

That combination produces metastability. A ring or blob may persist for many updates without being an immutable object. Individual particles can circulate through it, detach or be replaced while the large-scale organisation remains recognisable. The form can outlive its membership.

This is one reason the system appears lifelike. Living bodies also maintain organisation despite turnover of matter, but visual analogy is not mechanistic identity. Particle Life has no membrane state, metabolism or homeostatic controller. The intellectually defensible observation is that persistent organisation need not require permanent constituents.

The Chase fields preset is the clearest demonstration of nonreciprocity. Its structured matrix creates directed cyclic relations among types. The visible pursuit is not an animation track and not the result of goal-seeking code; it is the spatial consequence of mismatched pair responses.

The Rings & cells preset makes morphology easiest to see. Curved and hollow aggregates emerge when attraction, repulsion, density and motion balance. The word cell in the preset is morphological shorthand only. There is no represented membrane, inside/outside chemistry, osmotic pressure or reproduction. A “boundary” is a temporarily maintained particle arrangement.

The Soft dust preset is scientifically useful because weak coupling reveals what the stronger presets add. Particles remain relatively diffuse and slowly organise. Raising the Force multiplier from that baseline demonstrates that more coupling does not monotonically produce more stable order. Very strong interaction can make the world fast, turbulent and destructive. Self-organisation usually occupies a regime, not the maximum value of an “order” slider.

Turbulence further prevents the forms from becoming merely frozen force equilibria. It continuously perturbs velocity. At low values, structures may settle or persist more cleanly; at higher values, they continually deform, shed particles and reorganise. Randomness here is not the source of the interaction pattern, but it explores and destabilises the possibilities created by the matrix.

The species count changes the dimension of the relationship system. Two types permit a small set of attraction/repulsion relations. Six types create thirty-six directed entries including self-relations. Increasing the number of colours therefore enlarges the possible relational grammar, although a random matrix does not guarantee more meaningful organisation.

The world is toroidal. Particles crossing an edge re-enter from the opposite side, and interaction uses wrapped distance. As in Flock, this avoids wall accumulation but means the visible rectangle is not a bounded container.

The broader intellectual context is artificial life, a field organised around the synthetic study of lifelike behaviour in artificial media. Christopher Langton’s first workshop at Los Alamos in 1987 helped consolidate that programme. Particle Life fits the bottom-up method—construct minimal rules and study the behaviours they can support—but it occupies only a narrow part of the field. It lacks reproduction, heredity, adaptation, metabolism and evolution.

That is why Artificial Life would be a poor sphere name: too broad and too ontologically suggestive. Particle Life is the established name of this particular rule family and can be used responsibly when paired with the explicit distinction:

The system is lifelike without being alive.

The broad background is the synthetic tradition of artificial life. Christopher Langton characterised Artificial Life as the study of man-made systems exhibiting behaviours associated with natural living systems and contrasted biology’s analysis of life-as-we-know-it with the exploration of life-as-it-could-be. The 1987 Los Alamos workshop brought together earlier work on cellular automata, self-reproduction, artificial organisms and simulated ecologies.

Particle Life’s direct lineage is more specific.

Jeffrey Ventrella developed Clusters, which he describes as an asymmetrical particle system with emergent patterns. His account traces the idea back to earlier “microworld” experiments with independent attraction and repulsion responses. The key conceptual move was to allow asymmetric force fields between types, making the pair relation behave unlike ordinary Newtonian particles.

Tom Mohr explicitly credits Clusters as the original idea for Particle Life. He identifies his contributions as simplifying the rules while retaining complex behaviour, explaining them formally, and building an efficient reusable framework and simulator. His matrix documentation makes the directed type-pair logic especially clear.

The correct lineage is therefore not “someone discovered a new physical force.” It is:

artificial-life synthesis → Ventrella’s asymmetric Clusters → Mohr’s formalised Particle Life family → AL.Floys implementation and presets

The public title should preserve that recognised family name while the essay separates historical lineage from implementation-specific mathematics.

Aspect	Current implementation
Entities / field	Thousands of discrete particles divided into two to six type classes; no continuous chemical or biological field.
State	Position, velocity and species/type for each particle.
Update mechanism	Directed type-pair attraction/repulsion within a finite radius + weak very-short-range separation + turbulence → velocity retention and cap → position advance.
Relationship structure	A square directed matrix; each ordered type pair has an independent coefficient, including same-type relations.
Neighbourhood / interaction range	Fixed maximum radius, accelerated through a spatial hash.
Boundary conditions	Toroidal wrap for both movement and neighbour distance.
Randomness	Seeded initial positions/types/matrix and continuous turbulence.
Numerical approximation	Frame-scaled explicit updates, transformed matrix strength, configurable distance exponent, damping and hard maximum speed.
Rendering interpretation	Type colour, speed-sensitive streaks, trails, glow and optional velocity vectors. These do not create or store morphology.
Public simple controls	Population, Species, Max radius, Force multiplier and Trail persistence.
Public tools	Force, Spawn, Brush and Erase.
Canonical difference	AL.Floys uses its own smooth falloff, boost, anti-overlap and turbulence choices rather than reproducing one reference implementation byte-for-byte.

The default system uses 5,000 particles and six species. Those values make dense relational structure easy to see, but the governing principle is independent of the exact count.

Clustering — a collective object appears without an object class

Particles condense into aggregates even though the simulation defines only particles and pair rules. The cluster is an emergent statistical structure, not an entity stored in state.

Nonreciprocal pursuit — one colour follows while another flees

A directed matrix pair can create chase motion. The effect demonstrates how asymmetric local relationships generate apparently purposeful trajectories without purpose.

Rings and cell-like boundaries — geometry from competing interaction

Hollow, curved or rotating arrangements appear when different forces and motion balance. The visible boundary is a dynamic configuration, not a membrane.

Segregation and interfaces — type relations organise space

Some colours mix, others form separate domains or shells. Spatial sorting makes the hidden matrix partially readable from morphology.

Metastability — form persists while material changes

Track one ring or blob closely. Particles may exchange with the surroundings while the large-scale pattern survives. Organisation is not identical to a fixed set of constituents.

Range-driven fragmentation — connectivity sets collective scale

Lowering Max radius can break large structures into smaller local systems. The event reveals that the radius controls who can influence whom, not merely the size of a visual halo.

Reorganisation after disturbance — no blueprint is restored

A Force gesture can destroy a form. New structures emerge from the same rules but need not reproduce the old geometry, showing rule-based generativity rather than stored design.

First 30 seconds

1. Load Rings & cells.
2. Choose one hollow or curved structure and follow it rather than the whole screen. Ask whether its constituent particles remain fixed.
3. Lower Max radius well below the preset value, pause briefly if needed to compare, then return it toward the starting regime.
4. Watch large structures fragment and reconnect as the interaction network changes.
5. Load Chase fields and identify a pair of colours with visibly asymmetric pursuit.
6. Through Steer, use Brush to introduce or convert a small local patch to a neighbouring type and observe how its relationships change immediately.

Three experiments

Experiment	Question	Do	Watch for	Why it matters
Interaction horizon	How local can the rules remain while large forms survive?	Rings & cells → lower Max radius substantially → then raise it in stages.	Fragmentation, isolated micro-clusters and renewed large-scale coupling.	Shows that spatial organisation depends on interaction-network connectivity.
Coupling regime	Does stronger interaction always create more order?	Soft dust → raise Force multiplier gradually, changing nothing else.	Diffuse motion, then organisation, then possibly fast unstable rearrangement.	Demonstrates that organised regimes are not monotonic with force strength.
Asymmetric relationships	How can pursuit arise without goals?	Chase fields → use Brush on adjacent regions/types → let them interact.	One colour advances while another retreats or redirects.	Makes the directed matrix perceptually legible.

For the cleanest comparisons, hold Trail persistence constant. A longer trail can make pursuit easier to see, but it does not change the underlying relation.

Parameter	What it really controls	Increase it	Decrease it	What to watch
Population	Density of possible pair encounters.	More simultaneous interactions and denser morphology.	Sparser, more isolated dynamics.	Frequency and scale of aggregates.
Species	Number of type classes and therefore size of the relationship grammar.	More possible directed pair relations.	A simpler, easier-to-read matrix.	Diversity of sorting and pursuit patterns.
Max radius	The interaction horizon and instantaneous graph connectivity.	Larger coupled regions.	Fragmented local components.	Maximum scale of coherent forms.
Force multiplier	Overall magnitude of matrix-driven response.	Faster, tighter or more violent rearrangement.	Softer, slower organisation.	Stability versus overshoot.
Interaction matrix (advanced)	The core directed rule for every ordered type pair.	Entry-specific.	Entry-specific.	Pursuit, shells, mixing, exclusion and self-clustering.
Turbulence (advanced)	Continuous random velocity perturbation.	More restless turnover and break-up.	Cleaner settling and longer-lived forms.	Metastability and restructuring.
Friction / retention (advanced)	Fraction of velocity retained between updates. Values nearer one preserve motion longer.	Longer inertial persistence.	Faster damping.	Rotation and stream lifetime.
Force power (advanced)	Shape of distance falloff within the interaction radius.	Concentrates or reshapes where force is strongest, depending on implementation semantics.	Broadens the relative influence of distance.	Internal texture and boundary thickness.
Trail persistence (visual)	Duration of drawn motion history.	Longer visible trajectories.	Cleaner current positions.	Never call trails a pheromone or memory field.

The matrix is the most explanatory advanced control, but Max radius is the best simple public lever because it changes the relational topology while remaining visually immediate.

Rings & cells

The best introduction. Stable-looking curved forms make emergence, metastability and non-membrane “boundaries” easy to discuss. Compare radius changes from this regime.

Chase fields

The most scientifically important preset because it exposes nonreciprocity. Use it to replace anthropomorphic language—“they decide to chase”—with directed pair relations.

Soft dust

The best weak-coupling baseline. It makes the transition from diffuse movement toward organised interaction visible when Force multiplier is increased.

Prototype soup

A dense mixed regime that displays many simultaneous structures. Useful after the matrix concept is understood; initially it can be visually too rich for causal reading.

Frenzy soup

A strongly driven, fast regime. It demonstrates that complexity and activity do not necessarily equal stable organisation. It is more useful as a limit case than as the first preset.

Recommended learning order: Rings & cells → Chase fields → Soft dust → Prototype soup → Frenzy soup.

• Force adds a local attractive or repelling velocity perturbation. Use it to test structural recovery and sensitivity.
• Spawn inserts particles of the selected type. It changes local density and the set of directed relationships present.
• Brush changes the species/type of existing particles within its radius. Because type selects the matrix row, Brush alters their future dynamics, not merely their colour.
• Erase removes particles and can puncture a ring, isolate a component or reduce encounter density.

Brush is especially revealing here. In many visual systems, recolouring is presentation. In Particle Life, changing colour changes the particle’s interaction identity.

The title Particle Life does not imply abiogenesis, synthetic cells or actual organisms. The engine contains no membrane state, metabolism, genome, reproduction, heredity, development, natural selection or chemical reaction network. “Species” means a computational interaction class.

Its forces are not literal atomic, molecular or gravitational forces. They may be nonreciprocal; velocity is damped and capped; turbulence injects perturbation; the finite interaction radius imposes an artificial horizon.

Cell-like outlines are morphological analogies. A ring does not establish an inside/outside chemistry, a self-maintaining membrane or a living boundary.

The defensible conclusion is precise and substantial:

Simple local relationships can produce persistent forms and motions that look lifelike even when no life has been modelled.

Particle Life contributes nonreciprocal relationship as a generator of organisation. Flock reaches order through heading consensus; Gravity applies a common attraction law; Particle Life permits each type to respond differently to every other type. That directed relational grammar generates pursuit, sorting, transient morphology and structures whose identity is collective rather than constituent.

Foundational and primary lineage

1. Christopher G. Langton, “Artificial Life,” Los Alamos conference contribution (1987; proceedings published 1989). OSTI record.
2. Jeffrey Ventrella, Clusters: An Asymmetrical Particle System with Emergent Patterns. Project and technical introduction.
3. Tom Mohr, “About this Project,” Particle Life Simulator. Mohr credits Ventrella’s Clusters and describes his simplification and formalisation contributions. Project provenance.
4. Tom Mohr, Particle Life matrix settings. Documents separate matrix(i,j) and matrix(j,i) responses. Matrix documentation.
5. Tom Mohr, Particle Life accelerator documentation. Gives a reference force-function implementation and finite interaction logic. Accelerator documentation.

Modern context

6. Wolfgang Banzhaf et al., “What Is Artificial Life Today, and Where Should It Go?” Artificial Life 30(1), 1–15 (2024). DOI: 10.1162/artl_e_00435.