Power law vs the rainbow chart
The rainbow chart is a colour-band picture of Bitcoin's history that its own author calls a fun way to look at the past, with “no scientific basis”. Its original curve was fixed in 2014; when the price fell through the bottom band in 2022, it was redrawn. The power law is a regression refitted every night, with bands defined as plain multiples of the trend. Use the rainbow for a feel of the cycles, the power law when you need a number and its error bars.
Where the rainbow chart comes from
According to Blockchaincenter, which hosts the best-known version, the first rainbow charts were made by the Reddit user azop in 2014. The live version started in 2019 and borrowed a curve from a 2014 Bitcointalk post by the user trolololo, a “logarithmic regression” which, in the page's words, means the line flattens out over time. The formula given on the page is:
y = 2.9065 ln(x) − 19.493
The page does not define x, so we do not recompute it here. The coloured bands were then laid over the curve. The author is candid: the chart is “meant to be a fun way of looking at the historical long term price movements”, it is “not investment advice”, and “there is no scientific basis underpinning it”.
What happened in 2022
A curve fitted once, in 2014, has to keep working on data it has never seen. In 2022, with the price below $20,000, it did not: the price broke through the bands. The author first decided to “let it die”, then added an extra band without changing the formula, and on 21 November 2022 published a V2 with a new formula fitted on nine more years of data. The current version on the site is a “dynamic Power Law regression model” fitted to the price history since 2012, which the page reports at an R² of 94.3%.
That is not a scandal; it is what happens to every fitted curve when new data arrives. The difference is whether the refit is declared and mechanical, or done by hand after the line has visibly broken.
Log curve versus power law
On a chart with a logarithmic price axis and an ordinary calendar axis, both models look like a curve that keeps bending flatter. That is why the rainbow was called a logarithmic regression and why it ended up as a power-law regression: they describe the same slowing growth. The power law states it directly. Price is a power of the network's age in days since the genesis block, so on log-log axes it is a straight line, and both its coefficients are re-estimated from the full history every night (today the exponent is 5.64).
The bigger difference is in the bands. The rainbow's colours are a visual design, spaced for readability. The power law's bands are 0.4× and 3× the trend, two numbers you can test. Against today's fit, 90% of daily closes since 2010 sit inside those bands, and the bands themselves are on the page in numbers, so you can check them. Our track record page shows how often they held out of sample, and where they did not.
What each is good for
The rainbow chart is good at one thing: showing at a glance where the price sits in its long history, in a way anyone can read. It is not built to be measured, and its author says so. The power law is built to be measured: a fitted trend ($143,791 today), a distance from it (0.57× today), and an exponent with real uncertainty that drifts as data arrives. It is still only a description of the past, and it can break in the same way the rainbow did.
Frequently asked questions
Is the Bitcoin rainbow chart accurate?
What is the difference between the rainbow chart and the power law?
Why was the rainbow chart changed in 2022?
Can the power law break like the rainbow chart did?
More research
Sources
Numbers updated 20 October 2026 · Coin Metrics daily closes through 19 October 2026 · price $81,462 · trend $143,791