Showing posts with label bitcoin power law. Show all posts
Showing posts with label bitcoin power law. Show all posts

Tuesday, August 12, 2025

Bitcoin Power Law (by ChatGPT 5)

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

  1. Histogram of synthetic Bitcoin address balances (log–log) — shows a heavy tail.

  2. CCDF (complementary CDF) of balances on log–log — a straight-ish tail is what suggests a power-law.

  3. 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).


2) With the halving event for Bitcoin supply, tell me all about that. Show tables and graphs:



Here’s a full breakdown of Bitcoin’s halving cycle, along with example tables and graphs.

Key facts

  • Bitcoin starts with a 50 BTC reward per block (2009).

  • Every 210,000 blocks (~4 years), the block reward halves.

  • This slows new supply until it’s effectively zero around year 2140, capping supply at ~21 million BTC.

  • 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

  1. Block Reward Over Time (log scale) — clearly shows the halving “steps” that cut issuance in half each cycle.

  2. Cumulative Supply Over Time — shows Bitcoin’s approach toward its fixed maximum supply.


3) Is the having supply event every 4 years an example of a powerlaw?

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:

yxαy \propto x^{-\alpha}

or in growth form:

yxαy \propto x^\alpha

On a log–log plot, a true power law is a straight line.


Bitcoin halving pattern

  • The block reward halves every fixed number of blocks (210,000), so it follows:

Reward at halving n=50×(12)n\text{Reward at halving } n = 50 \times \left(\frac{1}{2}\right)^n

  • That’s exponential decay, not a power law.

  • On a semi-log plot (log y vs. linear x), halvings produce a straight line.

  • 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 \propto (time since launch)α^\alpha. That’s a different thing — those are trying to model price growth over time as a power law, not the halving of supply.

So:

  • Halving schedule → exponential decay (not a power law)

  • Some price models → may fit a power law over certain time ranges




Here you go — two views of the same halving schedule:

  1. Semi-log plot (log y vs. linear x) → straight line, showing exponential decay of block rewards.

  2. 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.

Monday, July 21, 2025

Bitcoin Power Law Divergence Banana Zone (%) by JimSixOneEight (TradingView PineScript Indicator) Jim618

This is from https://x.com/JimSixOneEight/ (Jim618)... kudos!

**********

//@version=6
indicator("Bitcoin Power Law Divergence Banana Zone (%)", overlay=false)

//Bitcoin Power Law Divergence - JIM SIX ONE EIGHT - FREE, OPEN SOURCE, Just link to : https://x.com/JimSixOneEight

days_since_genesis = (time - timestamp("UTC", 2009, 1, 3, 0, 0, 0)) / (1000 * 60 * 60 * 24)

power_law = 0.0
if days_since_genesis > 1
    power_law := 2.88 * math.pow(days_since_genesis / 1000, 5.82)

divergence_percent = 0.0
if close > 0
    divergence_percent := ((close - power_law) / close) * 100


plot(divergence_percent, "Price Divergence (%)", color.purple, 2)

hline(0, "Zero Line", color.gray, hline.style_dashed)

// Define transparent colors for background fills
// Transparency is the 4th parameter (0-255, where 0 is fully transparent, 255 is fully opaque)
color_bg_red_60_80 = color.rgb(255, 100, 100, 50) // Light red for 60-80% band
color_bg_red_80_100 = color.rgb(200, 0, 0, 50)   // Medium red for 80-100% band
color_bg_red_above_100 = color.rgb(150, 0, 0, 50) // Dark red for above 100%

color_bg_green_60_80 = color.rgb(100, 255, 100, 50) // Light green for -60 to -80% band
color_bg_green_80_100 = color.rgb(0, 200, 0, 50)   // Medium green for -80 to -100% band
color_bg_green_below_100 = color.rgb(0, 150, 0, 50) // Dark green for below -100%

// Plot horizontal lines and store their IDs for filling
id_h60 = hline(60, "+60% Line", color.rgb(255, 50, 50), hline.style_solid)
id_h80 = hline(80, "+80% Line", color.rgb(200, 0, 0), hline.style_solid)
id_h100 = hline(100, "+100% Line", color.rgb(150, 0, 0), hline.style_solid)
id_h_top = hline(150, "", color.new(na, 100), display=display.none) // An invisible upper boundary for the top fill

id_h_minus60 = hline(-60, "-60% Line", color.rgb(50, 255, 50), hline.style_solid)
id_h_minus80 = hline(-80, "-80% Line", color.rgb(0, 200, 0), hline.style_solid)
id_h_minus100 = hline(-100, "-100% Line", color.rgb(0, 150, 0), hline.style_solid)
id_h_bottom = hline(-150, "", color.new(na, 100), display=display.none) // An invisible lower boundary for the bottom fill


// Fill between the fixed horizontal lines
// Positive zones
fill(id_h60, id_h80, color=color_bg_red_60_80, title="Fill 60-80%")
fill(id_h80, id_h100, color=color_bg_red_80_100, title="Fill 80-100%")
fill(id_h100, id_h_top, color=color_bg_red_above_100, title="Fill >100%") // Fill from 100% up to an arbitrary high point

// Negative zones
fill(id_h_minus60, id_h_minus80, color=color_bg_green_60_80, title="Fill -60 to -80%")
fill(id_h_minus80, id_h_minus100, color=color_bg_green_80_100, title="Fill -80 to -100%")
fill(id_h_minus100, id_h_bottom, color=color_bg_green_below_100, title="Fill <-100%") // Fill from -100% down to an arbitrary low point

**********

Thursday, December 19, 2024

Any date from 2009 to 2051 Bitcoin Price (Log/Log) Power Law Growth Corridor

Use this table to find the price of Bitcoin on any given date up to the year 2051

This table shows the low, medium or high price based on the Bitcoin Power Law (Log/Log) Power Law Growth Corridor.

https://bbcdsatoshi.blogspot.com/p/bitcoin-power-law-any-dateprice.html

Monday, August 19, 2024

The Bitcoin Power Law: A few simple graphs and tables

In 10 years Bitcoin is expected to increase by at least 600%. This is the “touching cloth” support line according to the BTC PowerLaw:
$50,000 = $300,000
$100,000 = $600,000
$250,000 = $1.4 Million
$500,000 = $3 Million
$1 Million = $6 Million
In 10 years Bitcoin is expected to increase by at least 600%.


If you hold (hodl) your Bitcoin for 10 years, until 2033 then 1 Bitcoin will be no lower than $300,000 USD. This is according to the Bitcoin PowerLaw.
Called the “touching cloth” line… … Here is a 10-year graph (2024–2033) showing the lowest/support line for the Bitcoin price using the PowerLaw.
0-year graph (2024–2033) showing the lowest/support
Called the “touching cloth” line

Here is a table for the next 10 years (2024–2033) showing the lowest/support line for the Bitcoin price using the PowerLaw. This is a conservative way of looking at things.
0-year graph (2024–2033) showing the lowest/support

4-Year graph and table of the Log/Log Bitcoin Power Law. Shows “lowest/support” Bitcoin Price for halving years 2012–2048. This is all you need.


4-Year graph and table of the Log/Log Bitcoin Power Law

4-Year graph and table of the Log/Log Bitcoin Power Law

Inspired by the work of: @Giovann35084111 | @hcburger1 | @dotkrueger | @apsk32 | @math_sci_tech | + others

Tuesday, March 26, 2024

Lowest prices projected for Bitcoin on the 1st of January each year (Bitcoin Power Law Model)

Using the Bitcoin Power Law Model, these are the LOWEST (the floor) prices projected for Bitcoin on the 1st of January each year. 

These figures have been rounded down and are approximate:

2024 = $24,000

2025 = $35,000

2026 = $50,000

2027 = $70,000

2028 = $96,000

2029 = $130,000

2030 = $174,000

2031 = $228,000

2032 = $295,000

2033 = $375,000

2034 = $480,000

2035 = $600,000

2036 = $750,000

2037 = $930,000

2038 = $1,140,000

2039 = $1,390,000

2040 = $1,600,000

Bitcoin Power Law (by ChatGPT 5)

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 ...