Each of the 60 nodes is an organisation — a quantum-hardware startup, a university lab, a national metrology institute — placed at a random point in the plane. Two nodes are partners (an edge) if they fall within the partnership radius of each other — a real random-geometric graph, so nearby organisations are more likely to collaborate, unlike a purely random network. This is Watts' linear threshold model for cascades on a network (Watts, 2002): every node i has a random adoption threshold θᵢ, and it switches from "not adopted" to "adopted" once the fraction of its already-adopted partners reaches that threshold:
node i adopts when: (adopted neighbors of i) / (degree of i) ≥ θᵢ
Update rule (synchronous): all nodes are re-evaluated each tick t → t+1
using the adoption state at tick t, so a cascade unfolds one hop per step.
A handful of seed adopters (gold) start already-committed — think of them as the first consortium to sign a joint-development agreement. Whether their commitment spreads to the whole network or fizzles out after one or two hops depends on two knobs:
- Partnership radius — how far apart two organisations can be and still collaborate. A small radius keeps the graph sparse and fragmented; past a critical radius the giant component spans nearly every node and a single seed can percolate through the whole graph — the same connectivity threshold that governs giant-component formation in random-geometric graphs.
- Adoption threshold — how much peer commitment a node needs before it signs on. A low mean threshold makes almost any local majority enough to convert a node; a high one requires near-unanimous partner buy-in, which stalls the cascade even on a dense network (Watts calls this the "cascade window").
Press Compare 5 Seed Choices to run the exact same network and threshold distribution five times with five different random seed sets, without touching the visible graph — you'll typically see final adoption land anywhere from a contained fizzle (a few percent) to full diffusion (100%), purely as a function of which nodes happened to start committed. That sensitivity to initial conditions is the same tipping-point behaviour observed in real technology-diffusion and collaboration networks.