Bitcoin Power Law [LuxAlgo]

The Bitcoin Power Law tool is a representation of Bitcoin prices first proposed by Giovanni Santostasi, Ph.D. It plots BTCUSD daily closes on a log10-log10 scale, and fits a linear regression channel to the data.

This channel helps traders visualise when the price is historically in a zone prone to tops or located within a discounted zone subject to future growth.

🔶 USAGE



Giovanni Santostasi, Ph.D. originated the Bitcoin Power-Law Theory; this implementation places it directly on a TradingView chart. The white line shows the daily closing price, while the cyan line is the best-fit regression.

A channel is constructed from the linear fit root mean squared error (RMSE), we can observe how price has repeatedly oscillated between each channel areas through every bull-bear cycle.



Excursions into the upper channel area can be followed by price surges and finishing on a top, whereas price touching the lower channel area coincides with a cycle low.



Users can change the channel areas multipliers, helping capture moves more precisely depending on the intended usage.

This tool only works on the daily BTCUSD chart. Ticker and timeframe must match exactly for the calculations to remain valid.

🔹 Linear Scale

Users can toggle on a linear scale for the time axis, in order to obtain a higher resolution of the price, (this will affect the linear regression channel fit, making it look poorer).

🔶 DETAILS

One of the advantages of the Power Law Theory proposed by Giovanni Santostasi is its ability to explain multiple behaviors of Bitcoin. We describe some key points below.

🔹 Power-Law Overview

A power law has the form y = A·xⁿ, and Bitcoin’s key variables follow this pattern across many orders of magnitude. Empirically, price rises roughly with t⁶, hash-rate with t¹² and the number of active addresses with t³.

When we plot these on log-log axes they appear as straight lines, revealing a scale-invariant system whose behaviour repeats proportionally as it grows.

🔹 Feedback-Loop Dynamics

Growth begins with new users, whose presence pushes the price higher via a Metcalfe-style square-law. A richer price pool funds more mining hardware; the Difficulty Adjustment immediately raises the hash-rate requirement, keeping profit margins razor-thin.

A higher hash rate secures the network, which in turn attracts the next wave of users. Because risk and Difficulty act as braking forces, user adoption advances as a power of three in time rather than an unchecked S-curve. This circular causality repeats without end, producing the familiar boom-and-bust cadence around the long-term power-law channel.

🔹 Scale Invariance & Predictions

Scale invariance means that enlarging the timeline in log-log space leaves the trajectory unchanged.

The same geometric proportions that described the first dollar of value can therefore extend to a projected million-dollar bitcoin, provided no catastrophic break occurs. Institutional ETF inflows supply fresh capital but do not bend the underlying slope; only a persistent deviation from the line would falsify the current model.

🔹 Implications

The theory assigns scarcity no direct role; iterative feedback and the Difficulty Adjustment are sufficient to govern Bitcoin’s expansion. Long-term valuation should focus on position within the power-law channel, while bubbles—sharp departures above trend that later revert—are expected punctuations of an otherwise steady climb.

Beyond about 2040, disruptive technological shifts could alter the parameters, but for the next order of magnitude the present slope remains the simplest, most robust guide.

Bitcoin behaves less like a traditional asset and more like a self-organising digital organism whose value, security, and adoption co-evolve according to immutable power-law rules.

🔶 SETTINGS

🔹 General

• Start Calculation: Determine the start date used by the calculation, with any prior prices being ignored. (default - 15 Jul 2010)
  
• Use Linear Scale for X-Axis: Convert the horizontal axis from log(time) to linear calendar time
  

🔹 Linear Regression

• Show Regression Line: Enable/disable the central power-law trend line
  
• Regression Line Color: Choose the colour of the regression line
  
  
• Mult 1: Toggle line & fill, set multiplier (default +1), pick line colour and area fill colour
  
• Mult 2: Toggle line & fill, set multiplier (default +0.5), pick line colour and area fill colour
  
• Mult 3: Toggle line & fill, set multiplier (default -0.5), pick line colour and area fill colour
  
• Mult 4: Toggle line & fill, set multiplier (default -1), pick line colour and area fill colour
  

🔹 Style

• Price Line Color: Select the colour of the BTC price plot
  
• Auto Color: Automatically choose the best contrast colour for the price line
  
• Price Line Width: Set the thickness of the price line (1 – 5 px)
  
• Show Halvings: Enable/disable dotted vertical lines at each Bitcoin halving
  
• Halvings Color: Choose the colour of the halving lines