Defense in Depth: Gate Chain & Survival Decay

Defense Layers

Number of layers 4

Per-layer effectiveness 70%

Attack rate 8.0/s

Breach Statistics

P(breach) = (1 − 0.70)^4 = 0.81%

Attacks launched

Blocked

Breaches (core hit)

Empirical breach rate

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How it works

This is a 2D "gate chain" view of the same defense-in-depth math as the 3D concentric-sphere model: instead of nested shells, independent security layers are drawn as a chain of vertical gates that every attack packet must cross left-to-right to reach the core asset. Each gate stops a packet with probability p, checked independently the instant the packet spawns — exactly the sequential Bernoulli trial the formula describes.

P(breach) = (1 − p)^n
survival after k gates S(k) = (1 − p)^k
P(blocked exactly at gate k) = p·(1 − p)^k

The lower panel is new here: a live population-decay chart plots the theoretical survival curve S(k) next to the empirical fraction of launched packets that actually made it past the first k gates, binned in real time from the corridor simulation above. The two curves should converge as attacks accumulate — the same convergence the 3D version only reports as two numbers, shown here as a shape.

Layers slider — number of independent gates (n) in the corridor.
Effectiveness slider — per-gate stop probability (p), identical at every gate.
Attack rate — packets spawned per second at the left edge.
Each packet's fate is rolled once at spawn by walking the gates in order and stopping at the first one that blocks it — a packet that clears every gate reaches the core and counts as a breach.

Real-world relevance: security teams call this "layering" rather than relying on one control — a single 70%-effective gate is a near coin flip, but four independent gates in series push breach probability under 1%, which is exactly what both the corridor and the decay curve converge on below.

Attack packet Blocked at gate Core asset Theoretical S(k)

Defense in Depth: Gate Chain & Survival Decay (2D)