PhD Mentor-Tree Belief Drift Simulator

Mentor Tree

Tree depth (generations) 5

Branching factor (students / advisor) 3

Per-generation drift rate 35%

Lineage count (leaves)

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Total candidates

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Root belief

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Leaf-gen variance

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Belief variance by generation (0→leaf)

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Each PhD candidate inherits their advisor's methodological stance; drift is an independent coin-flip at every advisor→student hop, so variance only ever grows down the tree, never resets.

How it works

Every advisor has some number of PhD students (the branching factor), each of whom eventually advises their own students, forming a strict tree — one parent per node, no cross-links. This is unlike ufo-professors-pollution's scale-free hub network or ufo-schoolchildren-pollution's dense small-world classroom graph: here belief only ever flows one way, root to leaves, along a single path per lineage.

child belief:   b' = clamp(b + X·δ, 0, 1)
drift trigger:  X  ~ Bernoulli(driftRate)     (independent, per hop)
deviation:      δ  ~ Uniform(−Δ, +Δ),  Δ = 0.12
generation g:   hops from the root advisor (g=0) to a candidate

Belief axis — 0 = strict empiricist stance, 1 = strict theory-first stance. The scatter's color (blue→orange) tracks this value; the root starts at a random point on the axis.
Why variance only grows — because each hop's drift is independent and additive, Var(generation g) grows roughly linearly with g·driftRate·Δ²⁄3, the same random-walk accumulation behind genetic drift down a pedigree. A lineage can never "correct" back toward the root by itself.
Reading the plot — each column is one generation; the box marks the 25–75th percentile of belief in that generation, the tick is the mean, and dots are individual candidates (sampled for large generations). Watch the box widen as depth increases.
The tree is capped at ~4,000 candidates for performance — a deep, wide tree stops branching once the cap is hit and the remaining nodes are treated as leaves early.

Belief: empiricist → theorist Root advisor Box = 25–75th percentile