Real patent citation networks are not random — they grow by preferential attachment (also known as cumulative advantage, first modeled by Derek de Solla Price in 1976 and later generalized as the Barabási–Albert model). Every patent added to the system cites a handful of existing patents, and it is far more likely to cite a patent that is already heavily cited than an obscure one. A well-known, foundational patent keeps attracting new citations precisely because it is already well known — "the rich get richer."
This simulation runs that exact rule. Each new patent (node) picks its m citation targets using weighted random selection, where a patent's selection weight is its current citation count plus one (so a brand-new patent with zero citations still has a nonzero chance of being cited). As citations accumulate on a small number of nodes, those nodes visibly grow into large "landmark" spheres on screen — this is not scripted, it emerges purely from the weighted-random rule running thousands of times.
weight(patent i) = citations(i) + 1
P(new patent cites i) = weight(i) / Σ weight(all existing patents)
The payoff of running this rule for real is the citation-count distribution it produces: plotted on log–log axes, the fraction of patents with exactly k citations falls off as a straight line, i.e. P(k) ∝ k−γ — a genuine power law, the same empirically observed shape found in real patent, paper, and web-link citation data. The exponent γ shown on screen is fit live by ordinary least squares on the log–log histogram, so you can watch the estimate stabilize as more patents are added — this is the actual empirical signature of preferential attachment, not a decorative approximation.