Bitcoin Rainbow Chart — Logarithmic Regression Price Zones

What the bitcoin rainbow chart is

The rainbow chart is a long-term growth curve for the bitcoin price with colour-coded bands around it. It is built on a logarithmic regression: log10(price) = a · ln(days since the genesis block) + b. The curve is fitted to the full price history by least squares, and the zones are fixed-width bands above and below it. The logarithmic curve was introduced by the BitcoinTalk user Trolololo in 2014, the labelled colour bands were added by azop, and the familiar interactive version was built by Rohmeo on blockchaincenter.net.

How to read the zones

• Blue shades (“basically a fire sale”, “buy”, “accumulate”) — price well below the long-term curve. Historically these levels appeared at bear-market bottoms.
• Green shades (“still cheap”, “HODL”) — price near the curve, the market is in line with its historical trend.
• Yellow and orange (“is this a bubble?”, “FOMO intensifies”) — price above the curve, the market is heating up.
• Red shades (“sell”, “maximum bubble territory”) — an extreme departure from the trend, where cycle tops have historically occurred.

The nine zones divide the logarithmic corridor between the outer blue and red edges into equal segments on every date. The bands are therefore even in log10(price), while their price multiplier tightens with the cycle amplitude; the current width is shown in the card above the chart. Hover the chart to see the price, the model curve value and the zone for any date.

Halvings and the rainbow shape

The dashed vertical lines mark bitcoin halvings — the block reward being cut in half roughly every four years. The outer red edge passes through the known cycle highs (December 2013, December 2017, November 2021 and October 2025). The outer blue edge is one supporting logarithmic line: log10(price) = m · ln(days) + q. The model selects the two binding points from the lower convex hull of the complete daily series; the restored January 2015 low now participates directly in the calculation. The blue boundary therefore remains below the entire observed history but does not have to touch every cycle low: some bottoms correctly remain above it. There is no lower spline or wave, and the same logarithmic line continues into the forecast. This is not an extra line: all nine colour bands are stretched entirely between the two outer edges and have equal width in log space. The red-edge calculation is unchanged. The scale is logarithmic only: the model corridor is multiplicative and cannot be shown in full on a linear axis without flattening the early history into a sliver near zero.

An important caveat

The rainbow chart is not a forecast. It fits a curve to the past with no economic foundation: the model rests only on the assumption that growth slows logarithmically, and it can stop working at any time — as earlier versions of the curve already did and had to be refitted. The zones describe deviation from a historical trend, not a fair value. This page is informational and is not individual investment advice.