Adoption Power Law
Non-zero balance addresses compared with N(t) = 10^(a + b × log10(days_since_genesis)). Trinity refits a and b by ordinary least squares over all valid available history. The lower envelope uses the minimum log residual of this same fit; it is a historical boundary, not guaranteed support.
What is it?
Non-zero balance addresses compared with N(t) = 10^(a + b × log10(days_since_genesis)). Trinity refits a and b by ordinary least squares over all valid available history. The lower envelope uses the minimum log residual of this same fit; it is a historical boundary, not guaranteed support. The lower curve is N(t) × 10^min(r), with r = log10(observed addresses / N(t)). The public Santostasi and Perrenod work provides background; its published coefficients are not used in this Trinity fit.
How to read
Compare observed non-zero balance addresses with the fitted trend and its historical lower envelope on the address axis. The optional BTC price stays on its separate USD axis. Above or below the trend describes a level difference, not a growth-rate change. These are not daily active addresses.
Key zones
Above trend: more addresses than the fitted model. Below trend: fewer addresses. The lower envelope touches the lowest residual observed in the calibration history. It contains that history by construction and has no demonstrated role as support.
What to observe
A sustained plateau or prolonged departure from the trend means a single power law poorly describes that period. If later observations remain below a previously calibrated envelope, that envelope no longer describes them; do not interpret it as support. Refitting can change the past curves.
Historical context
Public research explores relationships between address growth, network value and age. This chart estimates its own descriptive coefficients from observed addresses, without assuming a cubic exponent or an epidemic mechanism.
Expert notes
Fit log10(N) = a + b log10(t) on every positive finite observation with positive network age. The lower multiplicative width uses the minimum residual of this fit, rather than a published fixed standard deviation. This retrospective envelope is sensitive to extreme observations and does not establish predictive accuracy.
Common mistakes to avoid
Addresses are not people: one person can control several addresses, and a custodial address can serve many people. A full-history fit is descriptive, not a point-in-time backtest. A power law cannot represent every plateau or structural break.
Programmatic access
REST API
curl -sS \
'https://api.trinityinsights.io/api/v1/onchain/metrics/adoption-power-law/data?timeframe=90d' \
-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.