loading lattice ▌
source
receiver
← zoan

Emitted random walk gravity

Interactive sketch of the cubic-lattice model in the paper. Drag to orbit, scroll to zoom.

tick0
walkers0
occupied sites0
registered arrivals0
mean kick xyz
angle to source
No walker is tracked one by one: each site keeps a count that splits six ways every tick. Paper: the mean force is exactly central, so the angle → 0° as arrivals accumulate.
source receiver walker packets kicks mean force lattice chunk
What you're seeing

The magenta source emits walkers every tick. Each walker takes one random step per tick along one of the six lattice directions (±x, ±y, ±z) and is never absorbed. Brighter packets carry more walkers.

Whenever walkers land on the cyan receiver, it gets a kick opposite their last step (magenta arrows, one per direction, sized by how many arrived that way). The walkers keep going.

The population thins out with distance from the source, so more arrive from the source side than the far side and the kicks don't cancel: their running mean (white arrow) settles toward the source. The paper shows this mean force is exactly central and approaches an inverse-square law at large separation.

Under the hood no walker is tracked. Each lattice site keeps a count; every tick that count is split six ways at random and handed to the neighbours, and the kicks are read off the directed arrivals. The paper proves this is exactly the same process as following every walker, which is why thousands of them cost no more than a few.

Didactic sketch of the rule in Appendix A and Section 6 of the paper, not a measurement of gravity and not the paper's numerical verification. Only a chunk of the infinite lattice is drawn; counts that wander far off are dropped.