This is the same boundary-defense model as the 3D packet-flythrough version, but drawn as its native mathematical objects instead of a spatial scene: a scrolling event ticker of individual packet outcomes, and a phase diagram of the closed-form compounding-probability formula.
Data diode: p = 0 (unidirectional at the physical/optical layer)
Firewall rule: p = leak slider value
P(≥1 breach in n attempts) = 1 − (1 − p)^n
The top panel is a live logic-analyzer-style trace: every attack attempt that reaches the boundary is drawn as a tick — green if blocked, red if it leaked through — and every telemetry reading (always allowed, OT → IT) is drawn as a blue tick on its own lane. This reproduces the exact same per-packet Bernoulli process as the 3D version's particle collisions, just rendered as a timeline instead of flying spheres.
The bottom panel plots P(≥1 breach in 20 attempts) = 1−(1−p)^20 as a curve over the leak probability p. A background Monte Carlo process — independent of the visual attack pace above, so it converges quickly regardless of the sliders — repeatedly draws batches of 20 independent Bernoulli(p) trials and records whether at least one leaked, then plots the empirical success rate against the same p. The two markers should sit on top of each other; the "Deviation" readout is |empirical − theory| and stays small (typically a few percent) because a 20-sample Bernoulli batch has standard error √(P(1−P)/trials), which shrinks as more trials accumulate.
- Attack intensity — rate of malicious command packets attempted from IT toward OT (drives the top ticker only).
- Telemetry rate — legitimate sensor/status readings flowing OT → IT (always allowed, both boundary types).
- Firewall leak probability p — per-packet chance a rule misconfiguration or parsing bug lets a command through; this is what the phase curve is plotted against.
- OT integrity — falls by a fixed amount per successful breach in the live ticker; only firewall mode can move it below 100%.
This is the same principle recommended by IEC 62443 / the Purdue Model for critical OT segments: unidirectional gateways at zone boundaries where the process must never accept remote write commands. A hardware data diode has no p to compound — the curve and the ticker both collapse to zero regardless of how many attempts are fired at it.