Bitcoin: power laws and log-periodic oscillations
BTC/USD on a log scale against two published power-law trend lines, plus two log-periodic waves least-squares fitted to the last 5 years of prices. The fit is recomputed with every daily data update. Drag the slider to run the curves out past 2030.
Combined-model peaks through 2032 (1)
| Date | Combined model | vs Perrenod baseline |
|---|---|---|
| 12 Jul 2030 | $2,022,080 | 4.72× |
How the model works
Two power laws in Bitcoin's age give the trend. Dacoinminster: price = 4.42×10−17 × days5.6, with days counted from the genesis block (3 Jan 2009). Perrenod: price = 0.00688 × years5.848.
On top of the Perrenod line sit two log-periodic waves, cos/sin(ω ln t) with ω = 2π / ln λ, for λ₁ = 2.081 and λ₂ = 1.305. Each cycle is λ times longer than the one before, so the swings stretch out as Bitcoin ages. Their amplitudes and phases come from an ordinary least-squares fit of log₁₀(price ÷ Perrenod) over 9 Nov 2021 to 9 Nov 2026. "Combined" applies both waves; "Average" is the mean of Oscillation 1, Oscillation 2 and Combined.
This is curve fitting, not a prediction, and it is not financial advice. The waves are fitted to five years of data and then extrapolated, often for decades. Small changes to the fit window move the forecast peaks by months and by large amounts of money. A power law can't keep going forever either: by 2100 the Perrenod line alone passes $2.10B per coin.
Credits and sources
This page brings together other people's work. We reimplemented it; the ideas and parameters are theirs.
- Dacoinminster power law: first published on the Bitcointalk forum by the user dacoinminster on 13 Feb 2013. The original fit was price = 4.41877×10−17 × days5.598 (rounded here to 4.42×10−17 and 5.6). Reported by TokenPost.
- Perrenod global power law and both log-periodic modes: Stephen Perrenod, Two-Year Scenario for Bitcoin: Two Log-Periodic Modes, Money or Debt Newsletter, 9 Aug 2026. The baseline price = 0.00688 × T5.848 and the scaling ratios λ₁ = 2.081 and λ₂ = 1.305 come from that post. Our fitted amplitudes are our own and may differ from his.
- Power law in time more broadly: the idea of modelling bitcoin's price as a power of its age is most closely tied to the physicist Giovanni Santostasi, who has worked on it since 2018, some of it with Perrenod.
- The notebook: the combined chart, the five-year fit window and the 2029–30 peak search follow an anonymous Python notebook posted to Pastebin on 9 Nov 2026. Its author didn't leave a name; if it's yours, get in touch and we'll credit you.
- Prices: the Bitcoin Weigh-In dataset (CC-BY-4.0). The extended horizon and the peak finder past 2030 are this site's own additions.