Smartphone Patch Gap 2D: N-Day Exposure Gas Simulator

Fleet & Rollout

Fleet size 80 devices

OEM/carrier patch delay 14 days

User update adoption 8%/day

Exploit released on day 30

Simulation speed 2.0 days/s

Live Status

Simulated day

Patched (simulated)

Patched (analytic model)

Actively exploitable now

Exposure (simulated)

0 dev-days

Exposure (analytic model)

0 dev-days

How it works

This is an independently-computed 2D counterpart to the 3D patch-gap fleet simulator: instead of a static grid of phones, the fleet is rendered as a real 2D gas of particles that collide elastically (momentum- and energy-conserving circle-circle collisions, just like billiard balls), while each particle's colour state is driven by the same real patch-adoption statistics used across the site's cybersecurity models:

day_available(i) = D_oem + jitter_i,  jitter_i ~ Uniform(0, 0.6·D_oem)
day_patched(i)   = day_available(i) + Geometric(a)   (a = daily adoption prob.)

What makes this 2D model genuinely distinct — not a flattened re-render — is that it also computes the closed-form expectation of the patched fraction directly, by numerically integrating the exact probability law over the jitter distribution, independent of any per-particle Monte Carlo run:

F(t) = E_j[ 1 − (1−a)^(⌊t−D−j⌋+1) ]  for t ≥ D+j, else 0
     ≈ (1/W)·Σ_s F_s(t),  W = 0.6·D, midpoint quadrature over j∈[0,W]

The dashed analytic curve plotted live in the corner overlay is F(t); the solid curve is the fraction actually patched among the bouncing particles on screen. They should track each other closely — any persistent gap would mean the simulation's random sampling disagrees with the theory. Cumulative exposure (device-days actively exploitable) is likewise reported both as counted from the particles and as the analytic prediction Σ_t=E^T N·(1−F(t)).

Colour key: blue = unpatched, no active exploit yet · red = unpatched while the exploit is live (actively exploitable) · green = patched and safe. Real fleets minimise the red region by shortening D_oem (fast vendor→OEM→carrier pipelines) and raising a (forced/auto updates, reminders) — the same two levers this simulator exposes.

Day 0

Unpatched (no active exploit) Unpatched & actively exploitable Patched

Simulated fraction patched Analytic model F(t)