Beekeeping Skill Adoption — 3D Bass Diffusion Network

Learner Network

Days per second 3.0

Innovation p 0.030

Imitation q 0.38

Learners N 100

Day

Adopted

0/0

F(t) sim

F(t) analytic

How it works

Every sphere is one learner, positioned on a Fibonacci sphere and peer-linked to its 3 geometrically-nearest neighbours. Each still-unskilled learner faces the exact same Bass diffusion hazard every simulated day: p (the course platform's own pull) plus q times F(t), the fraction of the whole network already skilled (peer word-of-mouth). Adoption is resolved node-by-node from that hazard, so the network's own count is the true F(t) — read out live next to the closed-form Bass solution for comparison. The instant a node adopts, a gold pulse physically flies along every one of its peer links, visualizing the word-of-mouth term actually reaching those neighbours.

dF/dt = (p + q·F)·(1 − F)
hazard(day) = p + q·F(t)
F(t) = (1 − e^-(p+q)t) / (1 + (q/p)·e^-(p+q)t)   [closed-form, p,q > 0]

Innovation p — adoption rate from the platform alone, no peers involved.
Imitation q — how strongly the already-skilled fraction pulls in the rest of the network.
Learners N — network size (fewer nodes = fewer, chunkier peer links).
Days per second — simulated time advance rate.

Real-world relevance: this is the network-level view behind the aggregate Bass S-curve — the same math a course platform uses to forecast uptake, but shown as the actual peer-to-peer process generating that curve, not just the curve itself.

Unskilled Skilled

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