Rainbow chart

The white line is bitcoin's closing price since 2010. The vertical axis is logarithmic: each step up is ten times the one below, so a rise from $100 to $1,000 takes the same height as one from $10,000 to $100,000. That is what lets the whole history fit on one chart without the early years lying flat on the floor.

Behind the price are nine coloured bands, from blue at the bottom to crimson at the top, under the names the original chart gave them: Fire sale, BUY!, Accumulate, Still cheap, HODL, Is this a bubble?, FOMO intensifies, Sell. Seriously. and Maximum bubble. The names are the chart's tradition and a joke about the market's moods, not instructions. Every band is equally tall on the log axis, and the whole rainbow bends and flattens as the years pass, because it is hung on a curve that grows ever more slowly.

The scale on the right is the rainbow in cross-section. At rest it lights the band today's price is in and marks how far up that band it sits; move across the chart and it follows the day under the cursor. Dashed verticals mark the halvings so far, and the legend switches them and the bands off. The chips above cut the chart to the last one, two, four or eight years, and on a computer you can drag across the plot to zoom and double-click to zoom back out.

The rainbow is a logarithmic regression. Perly fits one curve to every daily close in its record, of the form ln(price) = a · ln(b + days) + c, where days are counted from the first priced day. For each candidate b it solves a and c by least squares, and it keeps the b that leaves the smallest error, searching coarsely first and then finely around the best value. Nothing is copied from another site's chart: the fit is recomputed from the record every time the page is rebuilt, about every six hours.

The bands are hung on that curve at a fixed spacing. Each is 0.3 wide in natural logarithm, a factor of about 1.35 from its floor to its ceiling, and the fitted curve runs through the middle of the third band from the bottom, Accumulate. So the whole rainbow spans from a little under half the fitted value to about seven times it.

The rainbow chart as most people know it is Blockchain Center's, which laid coloured bands over a logarithmic regression of bitcoin's price and named each band after a mood of the market. Perly keeps the idea and the names, and credits them under the chart. Its bands come from its own fit to its own daily record, so they will not sit exactly where another site's do, and on a given day the band named here can differ from the one named elsewhere.

Because the fit uses the whole record, it is drawn with hindsight: the band shown for 2013 is the band today's curve puts 2013 in, not one anybody could have drawn at the time. Each new close nudges the curve a little, so a past day's band can change as the record grows, and the table is recomputed with every rebuild for the same reason.

The rainbow describes how the price has moved around one smooth curve. It is not a model of why bitcoin is priced as it is, and nothing obliges the price to stay inside it: the curve is only as good as the assumption that the coming years will look like the years since 2010. It reads best beside charts that measure something else — what the coins cost their holders, on the realized price and MVRV Z-Score charts, or how stretched the price is against its own averages, on the Mayer multiple and the 200-week average.