BTC Power Law [Financial 6-Pack | @itsToghrul]

A clean, research-grade roadmap for Bitcoin’s long-term trajectory. The script fits a power-law curve to BTCUSD price vs. days since genesis, adds asymmetric deviation bands to reflect diminishing upside, and can project the path forward while keeping chart clutter under control. A compact stats table shows model fit quality, live deviation, and model prices for a custom future date.

What it does

- Plots a base power-law model of BTC price over time.
- Adds an upper band that decays over time to capture diminishing returns, with multiple decay options.
- Adds a lower band as a fixed multiple to frame downside risk.
- Optionally boosts cycle peaks with Gaussian “bumps” to reflect halving-cycle dynamics.
- Draws dashed forward projections for the base line and bands over a user-defined horizon.

Displays a stats table with:

- Rolling R² of model vs. price (in log space) over a user-defined lookback.
- Current % deviation from the base model.
- Model, upper, and lower prices for a custom date you set.

Key features

- Five upper-band modes: Fixed, Exponential, Power-law, Stretched Exponential (Weibull), and Logistic/Hill. Each mode has intuitive controls for steepness, midpoint, floor, and reference scales.
- Cycle peak enhancer: Optional Gaussian sum with per-cycle decay, width, and period controls, plus an optional cosine modulation.
- Future projection controls: Choose the forward horizon in days and a sampling step to balance precision vs. performance. Projections render as transparent dashed lines to avoid clutter.
- Lightweight rendering: Internal caps on line segments keep drawings responsive without losing structure.
- Custom-date pricing: Build a date/time from parts and read off model, upper, and lower prices in the table.
- Transparent fit metric: Rolling R² in log space offers a quick quality check for the current regime.

Inputs overview

- Future projection: On/off, horizon (days), and sampling step.
- Colors: Base line and band colors with separate transparency for projections.
- Upper deviation: Mode selector plus parameters for decay shape, floor, reference scale, or midpoint/steepness, depending on mode.
- Lower deviation: Single fixed multiple with color.
- Gaussian peaks (optional): Amplitude base, cycle width, period, first-peak center, per-cycle decay, number of cycles, and optional cosine modulation.
- Stats: Rolling R² lookback length.
- Custom date: Year, month, day, hour, minute for quick scenario checks.

How to read it

- Base line: Long-term fair-value trend under a power-law regime.
- Upper band: Probable cycle top envelope that compresses over time. Switching modes changes how quickly headroom fades.
- Lower band: Defensive envelope for stress scenarios.
- Deviation %: Positive values signal overvaluation vs. model; negative values signal undervaluation vs. model.
- Custom date row: Quick “what-if” prices for your chosen timestamp.

Practical tips

- Use log scale on the price chart for visual clarity.
- For conservative tops, select Logistic/Hill or Stretched Exp with a non-trivial floor.
- For aggressive tops, use Power-law upper mode with a moderate exponent, then temper with the Gaussian enhancer.
- Keep the projection step coarse on lower-power machines to maintain snappy charts.
- Treat R² as a diagnostic, not a signal. Markets drift around regime shifts.

Intended use

Research and risk framing for BTC on higher timeframes. Works best on weekly or higher with reliable BTC spot pairs.

Disclaimer

Educational content only. No financial advice. Markets carry risk. Manage exposure and test ideas before acting.