The living snapshot — map decay

What it shows

The world model as a dynamic equilibrium between mapping and forgetting, rather than a monotonic record. With a positive decay rate the held map fades where it is not revisited; how much of the world the agent can hold at once depends on the balance between decay and revisit.

Setup

The P2 self-localized mapper, with OccupancyMap(decay=d): each cell's evidence decays each timestep (grid *= exp(-d·dt)); a whisker hit reinforces (+1, saturated at cap); the live map is the cells whose evidence exceeds thresh = 0.5. Two runs:

• a time-lapse at decay = 0.4/s, recording the live map at four moments during a 120 s exploration;
• a decay-rate sweep over decay ∈ {0, 0.05, 0.1, 0.2, 0.4, 0.8}/s, measuring the live coverage of the full arena at the end of each run.

Assumptions specific to this experiment

(in addition to the common and P2 sets)

• The occupancy map is no longer monotonic: cells lose evidence as exp(-d·dt) between hits.
• A live-cell threshold (0.5) with reinforcement cap (5.0) defines the "held" map. These knobs are configurable.

Run

cd experiments && ../.venv/bin/python p2_living_snapshot.py

Outputs

• figures/p2_living_snapshot.png — time-lapse (top) and decay-vs-coverage curve (bottom).
• printed summary.

Result & interpretation

Top: a time-lapse of the live map at decay 0.4 / s — a moving local snapshot that trails the agent and fades behind it. Bottom: live coverage of the full arena as a function of decay rate, falling from 99 % (accumulator) to 37 % at 0.8 / s.

At decay = 0 the map holds the full arena (~99 %). At 0.05/s it still does (half-life ≫ revisit period). From 0.1/s onwards coverage falls; by 0.8/s only ~37 % is held at a time — the map becomes a moving local snapshot that trails the agent and fades behind it. "The snapshot is always already becoming a different snapshot" turned into a measurable quantity.

decay (1/s)	half-life	live coverage
0.00	∞	99 %
0.05	13.9 s	99 %
0.10	6.9 s	91 %
0.20	3.5 s	73 %
0.40	1.7 s	52 %
0.80	0.9 s	37 %