1) Tell me about the Bitcoin power law. Give me example graphs:
I made three example graphs to illustrate different ways a power-law shows up in Bitcoin data.
• Power law = a relationship where P(X ≥ x) ∝ x^{-α} for large x (heavy tails). On log–log axes a pure power law is a straight line.
• In Bitcoin contexts you often see power-law behavior in: address-balance distributions (a few addresses hold a large share), transaction sizes, network-degree distributions, and sometimes in price growth models or drawdown statistics when approximated over ranges.
• Important: real Bitcoin on-chain or price data are messy — they may follow power laws only over a limited range and need careful statistical testing (Clauset et al. methods) to claim a true power-law.
What I produced
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Histogram of synthetic Bitcoin address balances (log–log) — shows a heavy tail.
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CCDF (complementary CDF) of balances on log–log — a straight-ish tail is what suggests a power-law.
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Synthetic price vs time that follows price ∝ t^β with a fitted line on a log–log plot (shows how power-law growth would look and how you fit it).
Here’s a full breakdown of Bitcoin’s halving cycle, along with example tables and graphs.
Key facts
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Bitcoin starts with a 50 BTC reward per block (2009).
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Every 210,000 blocks (~4 years), the block reward halves.
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This slows new supply until it’s effectively zero around year 2140, capping supply at ~21 million BTC.
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Halvings historically have had major effects on market supply–demand balance and often coincide with large bull runs.
Table of Halving Events (past + future)
| Halving # | Date | Block Height | Block Reward (BTC) | Coins in Period (BTC) | Cumulative Supply (BTC) |
|---|---|---|---|---|---|
| 0 | 2009-01-03 | 0 | 50.0000 | 50 | 50 |
| 1 | 2012-12-31 | 210,000 | 25.0000 | 5,250,000 | 5,250,050 |
| 2 | 2016-12-28 | 420,000 | 12.5000 | 2,625,000 | 7,875,050 |
| 3 | 2020-12-26 | 630,000 | 6.2500 | 1,312,500 | 9,187,550 |
| 4 | 2024-12-23 | 840,000 | 3.1250 | 656,250 | 9,843,800 |
| 5 | 2028-12-20 | 1,050,000 | 1.5625 | 328,125 | 10,171,925 |
| 6 | 2032-12-18 | 1,260,000 | 0.7813 | 164,063 | 10,335,988 |
Graphs
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Block Reward Over Time (log scale) — clearly shows the halving “steps” that cut issuance in half each cycle.
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Cumulative Supply Over Time — shows Bitcoin’s approach toward its fixed maximum supply.
Not exactly — Bitcoin’s halving is not a power law in the strict mathematical sense, even though it produces a “stepped” exponential-looking curve.
Here’s why:
Power law definition
A power law says something scales like:
or in growth form:
On a log–log plot, a true power law is a straight line.
Bitcoin halving pattern
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The block reward halves every fixed number of blocks (210,000), so it follows:
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That’s exponential decay, not a power law.
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On a semi-log plot (log y vs. linear x), halvings produce a straight line.
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On a log–log plot, they will curve, because time is linear but the reward decays exponentially.
Why people sometimes confuse the two
In Bitcoin price models, you sometimes see “power-law” charts where price (time since launch). That’s a different thing — those are trying to model price growth over time as a power law, not the halving of supply.
So:
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Halving schedule → exponential decay (not a power law)
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Some price models → may fit a power law over certain time ranges
Here you go — two views of the same halving schedule:
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Semi-log plot (log y vs. linear x) → straight line, showing exponential decay of block rewards.
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Log-log plot (log y vs. log x) → curved line, meaning not a true power law.
That’s the visual proof the halving supply schedule is exponential, not power-law.
