A boids steering rule: steer toward the average velocity vector of neighboring agents within a vision radius. Produces flocking cohesion of direction.

A point, line, or surface that pulls particles toward it — force typically proportional to inverse square of distance. Creates orbital and vortex behaviors.

A simulation composed of autonomous agents — each following its own local rules, with no global controller. Emergent behavior arises from agent interactions.

A simulated bird-like agent (Craig Reynolds, 1987). Exhibits flocking behavior through three local rules: separation, alignment, cohesion. The atomic unit of flocking simulation.

Random particle motion arising from thermal collisions. Modeled as a random walk — velocity perturbed by small random increments each frame. Produces organic, jittery drift.

A boids steering rule: steer toward the average position (center of mass) of neighbors within vision radius. Keeps the flock together without explicit tethering.

A friction force opposing velocity, proportional to speed. Applied as: velocity *= (1 - drag) per frame. Simulates air resistance, water viscosity, and general damping.

Complex, unexpected global patterns arising from simple local rules. The flock has no leader; the ecosystem has no script. Structure emerges from interaction alone.

The simplest numerical ODE solver: position += velocity * dt; velocity += acceleration * dt. Fast but accumulates error. Sufficient for visual particle simulations.

Collective motion of a group of agents following only local interaction rules. Produces murmuration-like patterns. Studied in starlings, fish schools, and pedestrian crowds.

A spatial function mapping position to a force vector — gravity (constant), wind (directional), turbulence (noise-based), vortex (rotational). Defines the invisible architecture particles navigate.

Differential equations modeling predator-prey population dynamics. Predator growth depends on prey density; prey declines with predator density. Produces cyclical population oscillations.

A scalar property of a particle. Determines resistance to acceleration (F=ma) and gravitational influence. Heavier particles accelerate more slowly and exert stronger gravitational fields.

A collection of discrete point-like objects (particles) each with position, velocity, mass, and visual properties, evolved over time by force equations. Invented formally by William Reeves (1983).

Smooth, continuous pseudo-random function (Ken Perlin, 1983). Produces coherent variation across space — used for turbulence, terrain, and noise-driven force fields.

An ecological interaction where predator agents hunt prey agents. Population cycles emerge: predators increase → prey decline → predators starve → prey recover. Classic Lotka-Volterra dynamics.

An attractor with negative force sign. Pushes particles away proportionally to proximity. Used for obstacle avoidance, explosion origins, and steering behaviors.

The three rules of boids: Separation (avoid crowding), Alignment (match velocity), Cohesion (move toward center). Together, sufficient to produce convincing flocking behavior.

A boids steering rule: steer away from neighbors that are too close, within a smaller separation radius. Prevents collision and overcrowding within the flock.

An autonomous agent behavior producing a steering force toward a desired velocity or position. Includes seek, flee, arrive, pursue, evade, wander, and flock. Coined by Craig Reynolds.

A more accurate integrator than Euler: updates position and velocity using average acceleration across the timestep. Better energy conservation — useful for orbital simulations.

A rotational force field where particles orbit a center point. Force is perpendicular to the radius vector (tangential). Produces swirling, cyclone-like particle paths.