N-Body Simulation

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What Is It?

This experiment is a field-mediated many-body system in a bounded two-dimensional cavity. Bodies do not attract each other through direct pairwise forces. Each body injects a compact local source into the grid. The field itself carries the interaction.

The animation title calls this “Gravity As A Message” because the influence travels through the mediator. The bodies do not know where the other bodies are. They only sample the local field gradient after the mediator has evolved by local update rules.

What It Tests

The experiment asks whether multi-body attraction, scattering and confinement-like behaviour can emerge when bodies interact through a finite-speed field rather than a direct all-to-all force calculation.

This makes it a useful bridge between clean field propagation experiments and more serious CAELIX body dynamics. If the field can carry coherent interaction structure here, later work can ask how burden, collision, motif extraction and substrate legality should replace the simplified floating-point carrier.

How It Works

A scalar field φ and velocity field v live on a discrete lattice. Each body stamps a compact local source into the grid. The mediator then evolves through a telegraph-style update with damping, local Laplacian propagation and source injection.

Each body samples the gradient of φ from a small ring around its own position. This ring sampling suppresses self-force from its own source stamp while keeping the acceleration lattice-derived. The body then moves by velocity-Verlet integration, with a soft cavity wall and a fail-safe clamp at the hard boundary.

The field itself is bounded by Dirichlet edges, where φ and v are clamped to zero. This makes the cavity explicit. Reflections, confinement and boundary pressure are therefore part of the experiment rather than hidden background assumptions.

What Is Not Hard-Coded

• No analytic 1/r potential is evaluated.
• No 1/r² force law is used.
• No pairwise body-to-body force calculation is performed.
• No precomputed orbital solution is imposed.

The bodies respond to the local mediator field. The only pairwise loop left in the code is for optional collision handling and field-derived spawn diagnostics, not for the main attraction law.

Why It Matters

Many-body demos are easy to fake with pairwise attraction. This experiment deliberately avoids that route. The interesting behaviour must travel through the field, lag through the update cadence and be shaped by the finite cavity.

For CAELIX, that makes the experiment a useful diagnostic. It shows what a field-mediated interaction can look like before the architecture moves to stricter integer balanced-ternary transport, SE/PE handoff and more explicit burden accounting.