For #Bitcoin,the power law has the exponent 6 and is derived from two other observed power laws in on-chain data:

a) growth of addresses over time, reflecting network adoption:

Addresses ∝ Time³

b) Price's quadratic response to adoption, aligning with Metcalfe's Law, which theorizes that the value of a network scales with the square of its connectivity:

Price ∝ Addresses²

If we approximate that Bitcoiners are synonymous with Addresses, we arrive at:

Price ∝ Bitcoiners² ∝ (Time³)² ∝ Time⁶

In addition, a power law relationship exists between Price and Hash Rate:

Hash Rate ∝ Price ² .

This relationship is due to the interplay between difficulty adjustment, Moore's Law, and halving events.

Studying #bitcoin....lessons cortesy of Giovanni Santostasi

his indicators below ...