The Bitcoin Rainbow Chart

Every Bitcoin daily close since 18 July 2010 sits on a logarithmic price axis, overlaid with an ordinary-least-squares regression of log₁₀(price) on ln(days since genesis). That fit is the centre line. Eight parallel offsets — fixed at 0.1 log₁₀ intervals above and below it — split the plot into nine coloured bands, each a 10^0.1 ≈ 1.26× multiplier of the one beneath. The gradient runs cool-to-warm: cool bands sit below trend, the centre band tracks the regression median, warm bands mark increasingly speculative territory. The colour is the whole idea — it turns a fifteen-year price series into a single glance at “cheap or hot, relative to trend.”

The input is one series: every Bitcoin daily close in USD (provenance on the sources page), matched to the deterministic day-count from the genesis block on 2009-01-03. The fit is log₁₀(price_i) = a · ln(days_i) + b + ε_i, solved by OLS over all 5,810 observations. Today’s coefficients are a = 2.4608, b = -16.4312, with R² = 0.9613. The nine bands are that line shifted by -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.3, 0.4 in log₁₀ space.

Two conventions are worth flagging, because most hosts leave them implicit. Days are counted from genesis (2009-01-03), not from the first traded price (2010-07-18), so the ln(days) axis tracks the protocol’s age rather than the market’s. And the regression refits every night, so the centre line and band edges move a little each day — the full derivation lives on the methodology page. Both choices match Blockchain Center’s canonical Rainbow.

Locate spot on the price axis, read across to today’s centre line, and note the log-space offset. Negative offsets put Bitcoin below the regression median in the cool bands (1 to 4) — historically the territory of cycle bottoms and multi-year accumulation. Positive offsets push it into the warm bands (6 to 9), where past tops and distribution phases have lived. Band 5 straddles the centre line: the model’s “no strong view” regime. Because the bands move on the order of weeks, the rainbow is a slow backdrop, not an entry signal — it tells you which third of the cycle you are in, not what next week does.

Applying today’s coefficients to each Bitcoin cycle extremum since 2013 surfaces a clear pattern. The 2013 and 2017 peaks saturate band 9; the 2021 peaks sit in band 9 but at shallower offsets; the 2024 pre-halving high registers only in band 6. Each top has landed at a shallower offset than the last. Prices are our own daily closes; band assignment uses the coefficients above.

The cleanest way to see it is log-space deviation at the four cycle tops:

• 04 Dec 2013 — spot $1,121.48, centre $102.02, log-space offset +1.04 (Euphoric).
• 17 Dec 2017 — spot $19,423.58, centre $3,042.93, log-space offset +0.81 (Euphoric).
• 10 Nov 2021 — spot $67,145.37, centre $23,598.04, log-space offset +0.45 (Euphoric).
• 14 Mar 2024 — spot $73,097.77, centre $60,905.42, log-space offset +0.08 (Elevated).

Log-space offset is a regression-scale invariant: when the slope flattens, the band boundaries flatten with it, so a constant offset would yield the same band reading cycle after cycle. These offsets are not constant — they are falling. Every cycle top has been less extreme, per Rainbow, than the one before it. That single observation is what most Rainbow hosts leave off the page, and it is the strongest argument against expecting the next top to reach where 2013’s or 2017’s did.

Under the current fit, every historical day is assigned the band it would sit in today. The distribution is asymmetric by design, and in practice more so than a flat 11%-per-band split: Bitcoin spends multi-year stretches in the lower bands and only brief windows in the mid-warm bands (6–8). The one exception is the topmost band 9, which is open-ended above and so absorbs every extreme high — it carries an outsized share despite holding only the blow-off peaks. That lower-band asymmetry is why a steady accumulation plan quietly works — most days are cheap-relative-to-trend days.

The regression slope flattens over time. Held static, the fit over-forecasts every future period — a 2018-vintage Rainbow would put the 2024 top in band 9, not band 6. Nightly refitting fixes that forward bias and imposes a backward one: historical peaks look more extreme than they did in real time, because the current fit is shallower than the one that was live on the day. Both biases are real, and both are the model’s shape rather than a bug in it.

The bands are descriptive, not predictive. Trolololo introduced the underlying regression in his 2014 BitcoinTalk thread with an explicit caveat — “just a model, not a crystal ball” — and Blockchain Center, who hosts the canonical version, frames it as a long-run reference, not a forecast. A reading inside a band does not imply mean reversion, and does not promise the return a past reading in that band produced.

It is one of many power-law-family models. The broader critique of log-regression fits on Bitcoin — laid out by Nico Cordeiro in his 2020 CoinDesk essay on stock-to-flow, and revisited in Giovanni Santostasi’s Power-Law Theory write-up — applies here. Bitcoin’s long-run price may or may not follow a power law; the Rainbow implicitly assumes it does. For the same shape with explicit confidence intervals rather than fixed log-offsets, the Power-Law Corridor is the cleaner instrument.

If you accumulate on a schedule, the chart asks nothing of you. The time-in-band asymmetry above does the work: a steady weekly buy lands disproportionately in bands 1–4 simply because that is where Bitcoin spends most of its days. There is no entry to time — the band structure already tilts a dumb schedule toward the cheap end.

If you are trying to time the cycle, treat the Rainbow as the slow backdrop and let faster instruments call the turn. Pair it with Pi Cycle for tops and the 200-week MA for floors; the rainbow alone moves on the order of weeks and will never give you a tight entry. And given the peak compression documented above, do not assume this cycle reaches the band a previous one did — that is the one forecast the chart actively argues against.