Orbital Drift

What to explore

Explore whether quantized local alignment creates common travel directions, separation, jams or persistent motion. Preserve literal quantization rather than adding hidden continuous steering or guarantees of convergence.

Rules, update order and replay

Square 80/120/160 lattice, toroidal by default, optionally bounded. Vacancies are empty; occupied positions hold one persistent organism with a heading 0–7. No birth, death, attraction, separation force or autonomous compass rotation occurs. Headings start uniformly seeded among N, NE, E, SE, S, SW, W, NW. Field and heading seeds are independent. Painting new life uses a seeded site stream.

One Step first freezes all positions and headings. Distance is Euclidean, using shortest wrapped displacement on a torus. Every other organism at d <= R counts once. Its weight is w = max(1, R-d)/R. For example, at R=20: d=20 contributes 1/20, d=10 contributes 1/2. The one-unit floor keeps the boundary influential; beyond R influence is zero. Radius is 1–32.

Compass vectors have unit Euclidean length, including diagonals. Let W=sum(w), A=sum(w*v_neighbor)/W and a=(strength/100)*min(1,W). The proposal is (1-a)v_self+aA. Strength is 0–100%, initially 100%. Normalizing combined influence prevents dense neighborhoods from extrapolating beyond their mean. For one neighbor at weight 1/2 the blend is exactly half-and-half. Direction is quantized immediately to the nearest of eight vectors. Cancellation and angular ties keep the prior heading (a 1e-12 numerical tolerance defines equality). There is no fractional heading retained between Steps. Close pairs may exchange headings or block instead of converging; that remains an observable consequence.

All headings commit together even when motion is blocked. Movement distance 1–4 means that many synchronous adjacent microsteps using the one newly chosen heading. At each microstep occupied sites, including departing occupants, block; bounded edges block; multiple claims on one empty destination all fail. Blocked organisms stop for the remainder of this Step; others continue. No retries, swaps, follow-through or tunneling. Crossing diagonal edges without a common lattice destination is allowed. One grid step along a diagonal traverses sqrt(2) geometric units, as in the collection's Moore movement convention. Population is conserved.

Reset rebuilds occupancy, headings, site streams, generation and evidence from the selected opening and both seeds. Clear empties the field and restarts streams. Painting existing occupancy preserves its heading; erasing removes it; new life draws a fresh seeded heading. Rule/topology edits preserve field/headings/streams, pause and invalidate evidence. Replay includes board, headings, streams, generation, carried previous heading/influence/movement evidence, rules and topology.

Reading the simulation

Canvas 2D uses eight named heading colors, optional heading strokes, and binary occupancy with Color off. Paused inspection shows current and proposed heading, each neighbor's distance/weight/heading, total influence, blended vector, tie reason, exact microstep outcome and next position, plus carried prior-Step evidence. Only the selected orbit is outlined. Written compass labels preserve meaning without color. Arrow keys select, Enter paints, P plays/pauses and S steps. One centered mobile all-rules action follows the stage instructions.