Deviation in Euclidean Distance from the Kaspa Power Law v3.0

🔶 First we need to understand what Power Laws are.

Power laws are mathematical relationships where one quantity varies as a power of another. They are prevalent in both natural and social systems, describing phenomena such as earthquake magnitudes, word frequencies, and wealth distributions. In a power-law relationship, a change in one quantity results in a proportional change in another, typically following a consistent and predictable mathematical pattern.

🔶 Why Do Power Laws work for Bitcoin and Kaspa?

Power laws work for Bitcoin and Kaspa due to the underlying principles of network dynamics and growth patterns that these cryptocurrencies exhibit. Here's how:

1. Network Growth and User Adoption:

Both Bitcoin and Kaspa grow as more users join their networks. The value of these networks often increases in a manner consistent with Metcalfe’s Law, which states that the value of a network is proportional to the square of its number of users. This relationship is a form of a power law, where network effects lead to exponential growth as more users participate.

2. Mining and Hash Rate:

The mining difficulty and hash rate in cryptocurrencies like Bitcoin and Kaspa adjust based on network activity. As more miners join, the difficulty increases to maintain a stable rate of block production. This self-adjusting mechanism creates feedback loops that can be described by power laws, ensuring the stability and security of the network over time.

3. Price Behavior:

Astrophysicist Giovanni Santostasi discovered that Bitcoin’s price follows a power-law distribution over time. This means that despite short-term volatility, Bitcoin’s long-term price behavior is predictable and adheres to specific mathematical patterns. Santostasi's model provides a framework for understanding Bitcoin’s price movements and forecasting future trends. He also discovered that Kaspa might be following a power-law aswell but it might be to early to tell because Kaspa hasn't been around for too long(2years).

4. Resource Allocation and System Stability:

As the price of Bitcoin or Kaspa increases, more resources are allocated to mining, leading to more sophisticated mining operations. This iterative process of investment and technological advancement follows a power-law pattern, driving the growth and stability of the network.

In summary, the application of power laws to Bitcoin and Kaspa offers a structured framework for understanding their price movements, network growth, and overall stability. These principles provide valuable predictive tools for long-term forecasting, helping to explain the dynamic behavior of these cryptocurrencies.

🔶 What does it look like on a chart?

Here is the Kaspa power law plotted on the KaspaUSD chart. Notice that the y-axis is in logarithmic scale. Unfortunately, TradingView does not allow the x-axis to be in logarithmic scale, which would otherwise make the power law appear as a straight line.

🔶 What is the deviation in Euclidean Distance from the Power Law?

Euclidean distance is a way to measure the straight-line distance between two points in a multi-dimensional space. When applied to a power law, it measures how far a data point is from the value predicted by the power-law formula.

🔶 Why are we measuring the Euclidean Distance from the Power Law & Discovery

On June 2, 2024, Plan C on Twitter announced a significant discovery: he and Dr. Giovanni Santostasi found that by examining the Euclidean distance from the Bitcoin power law, normalizing the data, and plotting it on an oscillator, it is possible to predict or time the market. In his post, Plan C hinted at the concept of "two-dimensional deviation," describing the result as the ultimate tool for navigating Bitcoin cycles. So, applying this technique to Kaspa, the only other cryptocurrency that might follow a power law might be a great idea!

This discovery leverages the power-law principles to create a sophisticated market timing tool, potentially offering insights into both Bitcoin and Kaspa's price movements.

🔶 Visual Representation of the Normalized Deviation in Euclidean Distance from the Kaspa Power Law

Steps Involved to visualize the indicator/oscillator:

1. Power Law Calculation:

The theoretical price is computed using the Power Law formula. This formula is based on the number of days since Kaspa's genesis block, simulating an ideal price growth trajectory.

2. Deviation Calculation:

For each day, the actual price is compared against the power law price for a range of days around the current date. The Euclidean Distance in days is the smallest number of days (either past or future) where this deviation is minimized.

3. Normalization:

The raw deviations over a fixed window are scaled to fit within a range of -100, 100. This normalized value is then smoothed using a simple moving average to produce a more readable oscillator.

4. Dynamic Coloring:

The oscillator's line color changes dynamically based on its value, providing an intuitive visual cue for traders.

🔶 Using the Oscillator

This indicator is best used on the Daily chart for KASUSD - crypto because it uses a power law formula based on days.

Identify Extremes:
When the oscillator shows high positive or negative values, it signals potential market extremes. This can help traders decide when to buy (when the market is oversold) or sell (when the market is overbought).

Values near -100 or 100 indicate significant deviation from the power law, highlighting potential market extremes.

🔶 Indicator Option's & Settings

Smooth Trends:
The smoothed line of the oscillator helps filter out market noise, allowing traders to focus on broader trends rather than short-term fluctuations.

Customize Your Analysis with Adjustable Price Sources:

One of the standout features of the Oscillator is its flexibility in using different price sources. You can customize the price source to better suit your trading style and analysis needs.

Price Source Selection:
The indicator allows you to choose the price source for its calculations. By default, it uses the average price of the daily candle (OHLC4), but you can adjust this to other price metrics such as the closing price, opening price, or any custom input.

Using Different Price Sources:
Using the daily candle average provides a balanced view of the day's trading activity, smoothing out intraday volatility.

Custom daily price sources:

Daily Highs:

Setting the price source to the daily high can help identify the maximum deviation when the market reaches its highest point during the day. This can be useful for spotting overbought conditions and potential resistance levels.

Daily Lows:

Conversely, using the daily low as the price source can highlight when the market hits its lowest point, indicating potential oversold conditions and support levels.

This flexibility ensures that the oscillator can be tailored to different trading strategies, allowing you to refine your analysis and make more informed decisions based on the price metrics most relevant to you.

By leveraging the Kaspa Power Law Deviation Oscillator, traders can gain a clearer perspective on market movements, making more informed decisions based on the deviation from a theoretically ideal price path. This tool adds another layer of insight to your trading strategy, helping you navigate the market with greater confidence.

🔶 LIMITATIONS

Like any technical analysis tool, the Deviation in Euclidean distance from the Kaspa Power law indicator has limitations. It's based on historical data, which may not always accurately predict future market movements.

發行說明

Deviation in Euclidean Distance from the Kaspa Power Law indicator updates:

-Now works on all timeframes
-Now works on all KASUSD tickers
-Added Buy & Sell signals based on long term Euclidean distance & Kaspa's cyclical behaviour.

發行說明

-Added the ability to switch easily between different powerlaw parameters/Genesis date.

發行說明

Updated pine version from 5 to 6.