Ω,D(Ω, D) DynamicsResearch library

Simple examples

Three laboratories, one information boundary.

Each example separates the actions available now, the continuity measure that ranks them, and the environment that acts only after a selection is made.

Explore the examples
01

Pool lab

A cue ball reaches the cushion.

Imagine the experimental cue ball moving toward the side of the table. The system is not asked to forecast every later bounce across the whole game.

Ω = {inertial roll, wall reflection, collision response, dissipative change}

D. D_info ranks the candidate next states by their local continuity: smoothness, energy and momentum consistency, contact constraints, and a small complexity cost.

“Which candidate next state is least discontinuous from the one I am in now?”

E. After that candidate is selected, the table applies friction and dissipation. That post-selection table response is E.

What this shows. The point is not that D rediscovers billiards from nothing. If the wall-reflection family is absent from Ω, D cannot invent it. The content is in the available action families; the ranking comes afterwards.

Open the Pool Lab
02

Stickman lab

A balancing figure has just been pushed.

Imagine the figure receiving a shove. It does not first model the floor, the exact force of the shove, gravity, and every possible later consequence.

Ω = {stance hold, idle sway, step recovery, arm windmill, crouch, walk step}

D. D ranks each candidate by closeness to a declared viable region: upright posture, balanced centre of mass, usable energy, and neutral joints.

“Of the actions I can express now, which one keeps me closest to balance?”

E. The chosen primitive is then passed to the physics step. Slipping, momentum, and the actual outcome of the push belong to E.

What this shows. This also exposes a demanding test: having the right name in Ω is not enough. The selected primitive must be able to realise a genuine recovery once the physics is allowed to respond.

Open the Stickman Lab
03

Minecraft lab

A survival agent stands near a ledge.

Imagine a Minecraft agent with low health and a dangerous edge nearby. The strict agent chooses from its declared primitives using its own state and a static local terrain snapshot.

Ω = {wait, turn, take a heading-relative step, use another declared survival primitive}

D. D measures distance from a survival manifold: staying alive takes priority, while health, hunger, position, facing, inventory, and locally visible terrain contribute through a declared metric.

“Which declared primitive keeps my present state closest to survival?”

E. Only after the choice does the live game tick run. Damage, hunger change, motion, and any outside event occur in E rather than inside the selector.

What this shows. The lab makes the boundary auditable: the selection side does not read live entities, fuses, falling blocks, or fluid flow. If those signals are admitted, that is a declared change to the model, not a hidden improvement.

Open the Minecraft laboratory