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Modeling Bitcoin Value with the Power Law and log periodicity
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- Sep 28, 2026
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Bitcoin as a Percolating Monetary Network: II (opens the original)
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Executive SummaryIn the first article of the series, we began to examine a simple proposition: fiat capital does not enter Bitcoin uniformly, but through a changing network of financial connections.Major expansions in U.S. Bitcoin access have historically preceded increases in global on-chain participation by approximately three quarters.The estimated relationship is economically meaningful as well as statistically strong. Across the full 2011–2026 history, a 10% increase in measured connectivit
The Current Bitcoin Bull Early Stage Mini-Bubble (opens the original)
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Tutorial on LPPLThe log periodic power law [LPPL] and the power law plus log periodicity [PL + LP] for Bitcoin are quite distinct models.The LPPL, most associated with Didier Sornette, is a 7 parameter model for individual market bubbles. So it is a shorter-to-intermediate time frame indicator.The power law [PL] describes Bitcoin’s long term scale invariant behavior, while log periodicity can be added to it +[LP] as a refinement for intermediate log time oscillations, known as discrete scale inv
Bitcoin as a Percolating Monetary Network: I (opens the original)
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This is the first in a series of articles examining a simple proposition: fiat capital does not enter Bitcoin uniformly. It enters through a changing network of financial connections.Those connections include exchanges, banks, trusts, futures markets, custodians, brokerage platforms, ETFs, OTC desks, stablecoin infrastructure, corporate treasuries, and individual buyers. Capital can reach Bitcoin only through channels that actually exist and are open to the relevant investors.That immediately su
Beyond the Power Law V: A Map of Bitcoin’s Hidden Geometry (opens the original)
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IntroductionOver four articles this summer I have been asking a question that goes beyond whether Bitcoin follows a power law:What kind of dynamical system produces the deviations around that power law?The long-run relationship itself is remarkably simple. Bitcoin price scales approximately asP(t) ~ tβ,with an exponent near Β ~ 5.7.That power law accounts for roughly 96% of the variation in log price over Bitcoin’s history.But the remaining few percent is not simply featureless noise.The four Be
Bitcoin’s Empirical Kelly Criterion (opens the original)
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IntroductionIn previous articles we have looked at Bitcoin’s Kelly allocation, usually using the Gambler’s Kelly, the original formula with discrete events. In a June article in Substack I noted, that despite decreasing return with the power law, due to the also declining volatility, Bitcoin’s continuous Kelly allocation is rising with time. This is a consequence of continuous Kelly placing variance, the square of volatility, in the denominator.The Kelly criterion is designed to maximize logarit
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