Each origami crane is an independent agent that steers using the classic Reynolds boids algorithm — the same three local rules driving the 3D version, ported here to a flat top-down view: separation (push away from flockmates closer than a short radius), alignment (steer toward the average heading of nearby flockmates) and cohesion (steer toward the average position of flockmates within a wider radius). No crane leads the group and no global rule dictates the shape of the flock — the wheeling, swirling flight pattern you see is emergent, produced purely by every crane following the same three rules using only what it can "see" nearby.
- Cohesion/separation strength scales both the pull toward the local flock center and the push away from crowding neighbors together, so pushing it up produces a tighter, more reactive flock and pulling it toward 0 lets the flock drift apart.
- Alignment strength scales how strongly each crane matches its neighbors' average heading — low values let sub-groups peel off in different directions; high values snap the whole flock onto a single heading.
- Order (heading align) is the Vicsek-style polarization order parameter |⟨cosθ,sinθ⟩| of the whole flock, from 0 (headings pointing every direction) to 1 (every crane flying the same way) — a live numeric read of how coordinated the flock currently is.
- Cranes wandering beyond the visible bounds feel a gentle pull back toward the center, keeping the whole flock on screen without a hard wall.