Forces to Flocks

A particle on a spring, stepped three ways: explicit Euler spirals out, semi-implicit Euler holds its orbit, Verlet hugs the exact curve. Why the order of two updates decides it.

Judge every pair of bodies by the boxes around the shapes first, give only the survivors the test their shapes need, and record each hit with the normal and depth a response pushes along.

File every point under the grid cell its coordinates floor to, then find who is near here by probing only the cells a radius can touch: the neighbour search behind flocks, collisions, and fluids.

A box that holds a few points and splits into four when it holds one too many: a tree fine where points crowd and coarse elsewhere, so a range query skips whole quarters of the field at once.

One body, one target, and one recipe: the behaviour names a desired velocity, the push is that minus the current velocity, capped. Seek, flee, arrive, wander, and pursue fall out of it.

Three local rules, each a capped steering force read off the neighbours in a circle, turn a scatter of boids into flocks nobody leads, splitting and merging round walls and obstacles.