OPEN-SOURCE SCRIPT
Bitcoin Power Law Bands | Astral Vision
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Bitcoin Power Law Bands | Astral Vision 🌠💠
Bitcoin's price history follows a remarkably consistent power law growth pattern, where the relationship between price and time, when both are expressed logarithmically, forms a structure that has held across more than a decade of market cycles. This indicator plots a full set of power law bands derived from that relationship, anchored to historically observed turning points across Bitcoin's complete price history, and converts the position of price within those bands into a normalized oscillator that makes the current cycle position immediately readable.
The power law model used here is time-segmented: rather than fitting a single static curve to all of Bitcoin's history, the model recalibrates its growth exponent across distinct historical phases, each anchored to a specific cycle low or high date. Each phase boundary is defined by a precise historical timestamp, and the local growth exponent h is interpolated continuously between these anchors using a base-4 progression. This segmented approach captures the documented deceleration in Bitcoin's growth rate as the asset matures, rather than assuming the same growth rate observed in the earliest years continues indefinitely.
The bands are constructed from the standard power law formula price = 10^(p1 + p2 × log10(h)), where h is the time-segmented exponent described above. Around this central curve, four bands are generated using a deviation term that itself decays as a function of h raised to a configurable power, multiplied by fixed standard-deviation-style coefficients (-3, -1.5, +4, +5) to produce the lower extreme, lower moderate, upper moderate, and upper extreme bands respectively. The decay structure means the bands compress proportionally as h grows, reflecting the empirical narrowing of Bitcoin's volatility envelope in log space over time.
The oscillator at the bottom of the indicator translates the absolute price position within these bands into a normalized 0 to 1 scale, where 0 represents the lower extreme band and 1 represents the upper extreme band. This transformation makes it possible to read Bitcoin's position within its long-term growth channel as a single number, comparable across any period in Bitcoin's history regardless of the dramatic difference in absolute price levels between, for example, 2015 and 2025.
The faded projection lines extending into the future use the same model structure carried forward from the most recent anchor, providing a visual reference for where the bands are mathematically projected to sit if the established growth pattern continues, without making any claim about whether price will actually follow that path.
This indicator is open-source. The full calculation, including the exact anchor timestamps, the segmented exponent interpolation, and the band deviation formula, is visible directly in the script for anyone who wants to study or build on the methodology.
Analytical Framework
Type of analysis: long-term structural growth modeling, cycle position assessment
Recommended timeframe: daily or weekly chart, for long-term position trading and cycle analysis exclusively. Not suitable for short-term or intraday use.
Signal type: deterministic power law bands with a normalized 0-1 position oscillator
How to interpret the signals
The candle coloring on the price chart provides the simplest read: when price closes above the upper moderate band, the candles take on the positive color, indicating Bitcoin is trading in the upper portion of its long-term growth channel, a zone that has historically corresponded to mid-to-late cycle conditions. When price closes below the lower moderate band, the candles take on the negative color, indicating Bitcoin is trading in the lower portion of its growth channel, a zone that has historically corresponded to deep value territory following major corrections.
The oscillator provides the same information with more granularity. A reading near 1.0 means price is pressed against the upper extreme of the historical growth channel, a condition that has, in every previous instance across Bitcoin's history, preceded a significant correction. A reading near 0.0 means price is pressed against the lower extreme, a condition that has, in every previous instance, marked one of the best long-term accumulation opportunities available. The two horizontal reference levels on the oscillator mark where the moderate bands sit on the normalized scale, making it easy to see when price transitions from the middle of the channel into either extreme zone.
Because the bands recalibrate their growth exponent at each historical cycle boundary, the position of price within the channel should be interpreted relative to the current cycle's specific band placement rather than assuming the same absolute price level carries the same meaning it did in a previous cycle.
How it differs from existing tools
Most power law indicators on TradingView fit a single static exponent across the entirety of Bitcoin's history, which forces a tradeoff between fitting the early years accurately and fitting recent years accurately. This indicator instead segments the growth model across historically anchored cycle boundaries, allowing the exponent to adapt as Bitcoin's growth rate has empirically decelerated. The normalized 0-1 oscillator is also a meaningful addition: rather than requiring visual inspection of where price sits between curved logarithmic bands, it converts that position into a single comparable number.
Plots 📊
Inputs 🎛️
This indicator has no configurable settings beyond color selection; all band parameters are fixed based on historical calibration and visible directly in the open-source code.
Colors 🎨
5 Astral Vision presets + custom override. Default: Futura.
Disclaimer ⭕️
This indicator is for informational and educational purposes only. It does not constitute financial advice. Past performance is not indicative of future results. Always do your own research before making investment decisions.
Bitcoin Power Law Bands | Astral Vision 🌠💠
Bitcoin's price history follows a remarkably consistent power law growth pattern, where the relationship between price and time, when both are expressed logarithmically, forms a structure that has held across more than a decade of market cycles. This indicator plots a full set of power law bands derived from that relationship, anchored to historically observed turning points across Bitcoin's complete price history, and converts the position of price within those bands into a normalized oscillator that makes the current cycle position immediately readable.
The power law model used here is time-segmented: rather than fitting a single static curve to all of Bitcoin's history, the model recalibrates its growth exponent across distinct historical phases, each anchored to a specific cycle low or high date. Each phase boundary is defined by a precise historical timestamp, and the local growth exponent h is interpolated continuously between these anchors using a base-4 progression. This segmented approach captures the documented deceleration in Bitcoin's growth rate as the asset matures, rather than assuming the same growth rate observed in the earliest years continues indefinitely.
The bands are constructed from the standard power law formula price = 10^(p1 + p2 × log10(h)), where h is the time-segmented exponent described above. Around this central curve, four bands are generated using a deviation term that itself decays as a function of h raised to a configurable power, multiplied by fixed standard-deviation-style coefficients (-3, -1.5, +4, +5) to produce the lower extreme, lower moderate, upper moderate, and upper extreme bands respectively. The decay structure means the bands compress proportionally as h grows, reflecting the empirical narrowing of Bitcoin's volatility envelope in log space over time.
The oscillator at the bottom of the indicator translates the absolute price position within these bands into a normalized 0 to 1 scale, where 0 represents the lower extreme band and 1 represents the upper extreme band. This transformation makes it possible to read Bitcoin's position within its long-term growth channel as a single number, comparable across any period in Bitcoin's history regardless of the dramatic difference in absolute price levels between, for example, 2015 and 2025.
The faded projection lines extending into the future use the same model structure carried forward from the most recent anchor, providing a visual reference for where the bands are mathematically projected to sit if the established growth pattern continues, without making any claim about whether price will actually follow that path.
This indicator is open-source. The full calculation, including the exact anchor timestamps, the segmented exponent interpolation, and the band deviation formula, is visible directly in the script for anyone who wants to study or build on the methodology.
Analytical Framework
Type of analysis: long-term structural growth modeling, cycle position assessment
Recommended timeframe: daily or weekly chart, for long-term position trading and cycle analysis exclusively. Not suitable for short-term or intraday use.
Signal type: deterministic power law bands with a normalized 0-1 position oscillator
How to interpret the signals
The candle coloring on the price chart provides the simplest read: when price closes above the upper moderate band, the candles take on the positive color, indicating Bitcoin is trading in the upper portion of its long-term growth channel, a zone that has historically corresponded to mid-to-late cycle conditions. When price closes below the lower moderate band, the candles take on the negative color, indicating Bitcoin is trading in the lower portion of its growth channel, a zone that has historically corresponded to deep value territory following major corrections.
The oscillator provides the same information with more granularity. A reading near 1.0 means price is pressed against the upper extreme of the historical growth channel, a condition that has, in every previous instance across Bitcoin's history, preceded a significant correction. A reading near 0.0 means price is pressed against the lower extreme, a condition that has, in every previous instance, marked one of the best long-term accumulation opportunities available. The two horizontal reference levels on the oscillator mark where the moderate bands sit on the normalized scale, making it easy to see when price transitions from the middle of the channel into either extreme zone.
Because the bands recalibrate their growth exponent at each historical cycle boundary, the position of price within the channel should be interpreted relative to the current cycle's specific band placement rather than assuming the same absolute price level carries the same meaning it did in a previous cycle.
How it differs from existing tools
Most power law indicators on TradingView fit a single static exponent across the entirety of Bitcoin's history, which forces a tradeoff between fitting the early years accurately and fitting recent years accurately. This indicator instead segments the growth model across historically anchored cycle boundaries, allowing the exponent to adapt as Bitcoin's growth rate has empirically decelerated. The normalized 0-1 oscillator is also a meaningful addition: rather than requiring visual inspection of where price sits between curved logarithmic bands, it converts that position into a single comparable number.
Plots 📊
- Four power law bands on the price chart: upper extreme, upper moderate, lower moderate, lower extreme
- Faded future projection lines extending the band structure forward
- Candle coloring on the price chart reflecting current position relative to the moderate bands
- Normalized 0-1 oscillator in the sub-panel with reference levels marking the moderate band positions
Inputs 🎛️
This indicator has no configurable settings beyond color selection; all band parameters are fixed based on historical calibration and visible directly in the open-source code.
Colors 🎨
5 Astral Vision presets + custom override. Default: Futura.
Disclaimer ⭕️
This indicator is for informational and educational purposes only. It does not constitute financial advice. Past performance is not indicative of future results. Always do your own research before making investment decisions.
Script de código aberto
Em verdadeiro espírito do TradingView, o criador deste script o tornou de código aberto, para que os traders possam revisar e verificar sua funcionalidade. Parabéns ao autor! Embora você possa usá-lo gratuitamente, lembre-se de que a republicação do código está sujeita às nossas Regras da Casa.
My premium indicators are available on Whop:
whop.com/astralvision
Astral Vision 🌠💠
whop.com/astralvision
Astral Vision 🌠💠
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.
Script de código aberto
Em verdadeiro espírito do TradingView, o criador deste script o tornou de código aberto, para que os traders possam revisar e verificar sua funcionalidade. Parabéns ao autor! Embora você possa usá-lo gratuitamente, lembre-se de que a republicação do código está sujeita às nossas Regras da Casa.
My premium indicators are available on Whop:
whop.com/astralvision
Astral Vision 🌠💠
whop.com/astralvision
Astral Vision 🌠💠
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.