Price Trend Power-law channel Median path 50% / 90% from today

replay the past

—

Bitcoin price snapshot

—

Trend today

—

the power law's central value

vs. trend

—

Schedule

—

price = trend value of that date

Channel position

—

cheapest daysbubble peaks

The decomposition — why 5.6?

The paper's finding: the price exponent factors into an adoption epidemic times the wealth pyramid it climbs. Both halves are measurable — here they are, refit live like everything else. (Always in USD — the pyramid is a dollar-wealth statement, whatever unit the chart above uses.)

Adopters grow as t^–

addresses with balance vs. age (log–log) — the idea-epidemic; dashed = power-law fit

Price grows as N^–

price vs. adopters (log–log) — each wave taps deeper pockets; dashed = power-law fit

On the timeline: one multiplies the other

Price Adopters alone (flat wallets, ∝ N) Adopters × wealth pyramid (∝ N^–)

Both curves start together in 2010. If every new adopter brought the same money, price would have grown like the crowd (navy). Each wave reaching deeper pockets multiplies that by N^0.84 — the widening gap — and lands on the actual price.

—

Year-by-year table (price, trend, and honest projection range)

Jan 1	Price	Trend	vs. trend	90% probable range

The law

P(t) ∝ t^5.6

Since its first traded price, bitcoin has followed a straight line on log-log axes: price grows as a fixed power of its age t (years since the genesis block, Jan 3 2009). Switch the chart to log time to see the line. Why ~5.6? An idea-epidemic spreading as t³ through a Pareto wealth pyramid — the decomposition is the story and the paper.

Honest error bars — what other charts hide

Most power-law sites draw razor-sharp lines decades into the future. But the residuals around the trend are four multi-year bubbles, not thousands of independent points — statistically the 16-year fit is worth about six observations, so the exponent is 5.6 ± 0.2, not ± 0.02.

The projection here shows what the data honestly implies. The fan starts at today's price — tomorrow won't be far from today — opens like a random walk, then relaxes toward the historical channel with the ~10-month half-life measured on the deviations. Band widths are calibrated horizon by horizon so that 50% / 90% of comparable historical episodes actually stayed inside, with the exponent's honest ±0.21 folded in on top. No false precision, no razor lines.

What 50% and 90% mean. Pick a date on the chart. Among past stretches of the same length, half of them ended inside the inner range and nine in ten inside the outer one. That is a statement about odds, not a wall: a wider range always buys better odds and worse precision. The band's edge is where we stopped drawing, not where the price stops going — switch the chart to Cloud and the same forecast is drawn as the whole distribution instead of two edges: dark where the price should spend most of its time, thinning outward, stopping nowhere. The price has left the 90% range before, and will again.

Reading the dials

vs. trend — how far today's price sits from the central line. Channel position — where that deviation ranks against every day since 2010 (0% = deepest discounts, 100% = bubble peaks). Schedule — the date whose trend value equals today's price: how far ahead of or behind the curve bitcoin is trading.

The model is refit in your browser from the full daily history on every load — no hard-coded magic numbers.