Bait Ball.

the rules

No fish sees the school. Each one steers on what’s inside a ~40 px bubble around it:

• separation — don’t crowd the neighbor in front of you
• alignment — swim roughly the way nearby fish are swimming
• cohesion — drift toward the local center of mass
• fear — anything big and amber within 120 px overrides everything else

That’s the whole controller. Nobody leads, nobody has a map, and the school you see is not programmed anywhere — it’s what those four urges add up to.

Predators run pure pursuit with a velocity lead, lunging when close. They’re faster than fish in a straight line but force-limited in turns, so the school’s agility is its defense. After a catch they’re satiated for a couple of seconds — which is exactly when the school reforms.

what to look for

• flash expansion — a predator strikes into the school and it detonates radially around the strike point
• fountain effect — fish split around the attacker and regroup behind it, where it can’t turn
• the bait ball — under sustained pressure the school packs into a dense, rolling ball

• φ in the HUD — the polarization order parameter,

  Σv̂

  /N. A perfectly aligned school reads 1.0; leaderless milling reads near 0. Set predators to zero and watch it climb; add them back and watch structure return.

notes

The cursor is a soft threat — the fish would rather you kept your distance, which means you can herd them. Simulation steps at a fixed 60 Hz with a seeded PRNG, so a run is reproducible; reset rerolls the seed. Neighbor queries go through a uniform spatial hash, which is the only reason 800 fish is a slider option and not a slideshow.