Bitcoin’s Power Law Curve — Fairly Valued With Room to RunThis chart applies a Power Law Rainbow Model to Bitcoin using a long-term logarithmic regression fitted to BTC's historical price action. Power laws are mathematical relationships often found in nature, science, and network systems — and Bitcoin is no exception.
Rather than relying on arbitrary trendlines, this model fits a curve based on the equation:
Price = a × t^b
Where:
t is the number of days since inception
a and b are constants optimized to Bitcoin's growth
Bands represent log-scaled standard deviation zones from the curve
🌈 Interpreting the Chart
The center white curve reflects Bitcoin's "fair value" according to its adoption-based trajectory.
Colored bands represent ±1σ, ±2σ, ±3σ from the model, creating a "valuation rainbow."
Historically, Bitcoin's cycle bottoms have touched the lower bands (blue/purple), while euphoria tops align with the upper bands (orange/red).
✅ Current Outlook
BTC is trading just under the fair value curve , suggesting it's fairly valued or slightly undervalued from a long-term perspective.
This position has historically preceded major upside moves, especially in post-halving environments.
From a Smart Money Concepts angle, we're in a potential accumulation or markup phase , with institutional and informed capital likely already positioning.
🧠 Why Power Laws Work for BTC
Bitcoin adoption follows network effects — more users = more value — which naturally follows a power law.
Unlike linear trends, power law curves scale with time , making them ideal for modeling exponential assets.
They offer a more objective long-term valuation framework , avoiding emotional cycle chasing.
⚠️ Disclaimer
This is not financial advice . The model reflects historical behavior and is a tool to support long-term perspective — not short-term prediction. Always do your own research and risk management.
