Adoption Power Law
Bitcoin address growth follows a cubic power law (N ∝ t³), consistent with epidemic spreading on scale-free networks. Derived from Santostasi & Perrenod (2026).
What is it?
The Adoption Power Law (Santostasi & Perrenod 2026, Eq. 2) shows that the number of non-zero-balance Bitcoin addresses grows as N(t) = 10^(-3.591 + 3.046 × log₁₀(t)), with R² = 0.977 across 5,696 observations. The cubic exponent (~3) is remarkable: it exactly matches the epidemic spreading model on scale-free networks (Colgate et al. 1989, AIDS). Bitcoin adoption propagates like a 'virus' from highly connected hubs (technically sophisticated early adopters) to less connected nodes (mainstream users).
How to read
The blue curve shows actual active addresses. The orange curve is the theoretical t³·⁰⁵ trend. When addresses are above the trend, the network is growing faster than the model - typically during bull markets. Below, growth is slowing - typically during bear markets. The red +1σ band marks adoption excess.
Key zones
Above trend: accelerated adoption (bull market, new entrants). On trend: normal organic growth. Below: temporary contraction (bear market, dust address purge).
What to observe
Sub-exponential growth (t³ instead of exponential) means the growth rate is CONTINUOUSLY decelerating - the network grows but ever more slowly. This is the 'saturation wave': hubs saturate, the adoption front diffuses to less connected tiers. The 0.046 excess above 3 may reflect differences in Bitcoin's connectivity distribution versus classic epidemic networks.
Historical context
The model places Bitcoin in the same universality class as HIV spreading (Colgate 1989) and biological growth. The exponent 3 = 1+1+1 arises from: one power for initial infection ramp-up, one for incubation-time convolution, one for integrating incidence into cumulative cases. This connection between technological adoption and epidemiology is a fundamental result of complex network theory.
Expert notes
This chart is the FIRST LEG of the Power Law decomposition. Combined with Metcalfe Fair Value (second leg), together they reconstitute the 5.69 price exponent. If the adoption exponent falls significantly below 3, the Power Law model would be falsified - this is one of the paper's explicit falsifiability conditions.
Common mistakes to avoid
Do not confuse active addresses with users - one user can control multiple addresses. Address growth is a proxy, not an exact adoption measure. The cubic model will eventually hit saturation (logistic S-curve) - the question is when, not if.
Programmatic access
REST API
curl -sS \
'https://api.trinityinsights.io/api/v1/onchain/adoption-power-law/history?days=90' \
-H 'X-API-Key: $TRINITY_API_KEY'MCP server
{
"tool": "get_chart_value",
"metric_id": "adoption-power-law",
"timeframe": "1y"
}Required tier: pro. See the pricing grid for the tier list and the MCP documentation for multi-client configuration.
Related metrics
Institutional disclaimer
Trinity Insights is an educational and analytical tool. The metric above does not constitute investment advice. Trinity Insights is not a Crypto-Asset Service Provider (CASP) registered under MiCA Regulation (EU) 2023/1114. See the full disclaimer.