BTC_POWER_LA

Think carefully about what this chart is showing. It contains the exact same data as the real Bitcoin chart. Nothing has been added, nothing has been removed. The only difference is that the values have been reordered from low to high.
Now imagine that this had been the actual historical path of Bitcoin. The price would always appear to go up, sometimes more slowly, sometimes more rapidly, but always upward. It would feel smoother, safer, more reassuring. In fact, most people would probably describe it as an extraordinary and remarkably comfortable journey.
And yet, mathematically, nothing has

Imagine I sort all the prices from lowest to high and then I plot them in a log log chart. The power law is clearer then ever.

This is an interesting graph. For each day we measure how far is the day from the previous all time high.
It shows a clear pattern: the steady power law growth and the size and durations of the drawdowns.

Is the Bitcoin bottom in August?

TradingView Indicator based on the complex exponent power law.

The Power Law Slope Signal to Noise ratio wants to get out of this transition zone to bullish behavior.
Just saying.

Updated log-periodic model with confidence level to 1 sigma.
I wouldn’t put too much weight on the exact values of the tops and bottoms, but the timing may be more meaningful. According to the model, the next bottom is around August of this year.
What I find compelling about this approach is that it uses a single power law with a complex exponent, rather than imposing an external cycle. In this framework, the oscillatory behavior emerges naturally from the data itself as part of the power-law structure.
The model fits the data well up to the present. The key question, as always, is whether th

There is something almost absurd about it, once you see it.
Even when Bitcoin's price deviates from the reference power law — trading above or below the central trend — it tends to move parallel to it.
The trajectory shifts, but the slope holds.
This is because what matters is not where you are on the chart, but which direction you are moving.
The power law defines a direction in log-space. And Bitcoin, stubbornly, keeps moving in that direction.

Several people noticed that the log-periodic model doesn't catch the current drawdown. I asked if a 6th peak could explain it. But it doesn't.
The 5-peak damped model predicts the current price at ~$156k — the actual is ~$71k, a gap of 0.28 dex.
Adding the 6th component (ω ≈ 5.15, corresponding to a longer sub-harmonic cycle with λ ≈ 3.4) improves the overall R² marginally from 0.751 to 0.797, but at the current moment it makes the prediction worse, not better — it actually pushes the model to predict ~$175k.
Two possible interpretations, none of which require adding parameters:
1) Pure nois

If you add a damping term then the model is really good.

Could we have seen this coming?
Fitting a repeating pattern from just three cycles is genuinely hard. Think of trying to identify the rhythm of a song from hearing only three beats — you can make a reasonable guess, but you won't be certain. That is roughly the situation here.
Yet something important shows up in the Figure below. The spectrum computed from Bitcoin data up to mid-2018 — before the 2021 cycle even began — already shows the same dominant frequency we recover from the full fifteen years of data. The fundamental oscillation was already clearly encoded in the first half of the histo