Advanced Fractal and Hurst IndicatorAdvanced Fractal and Hurst Indicator (AFHI)
Description:
The Advanced Fractal and Hurst Indicator (AFHI) is a custom technical analysis tool designed to identify market trends and potential reversals by leveraging the concepts of Fractal Dimension and the Hurst Exponent . These advanced mathematical concepts provide insights into the complexity and persistence of price movements, making this indicator a powerful addition to any trader's toolkit.
How It Works:
Fractal Dimension (FD) :
The Fractal Dimension measures the complexity of price movements. A higher Fractal Dimension indicates a more complex, choppy market, while a lower value suggests smoother trends.
The FD is calculated using the log difference of price movements over a specified length.
Hurst Exponent (HE) :
The Hurst Exponent indicates the tendency of a time series to either regress to the mean or cluster in a direction. Values below 0.5 indicate a tendency to revert to the mean (mean-reverting), while values above 0.5 suggest a trending market.
The HE is calculated using the rescaled range method, comparing the range of price movements to the standard deviation.
Composite Indicator :
The Composite Indicator combines the smoothed Fractal Dimension and Hurst Exponent to provide a single value indicating market conditions. This is done by normalizing the FD and HE values and combining them into one metric.
A positive Composite Indicator suggests an uptrend, while a negative value indicates a downtrend.
Smoothing :
Both FD and HE values are smoothed using a simple moving average to reduce noise and provide clearer signals.
Trend Confirmation :
A 50-period moving average (MA) is used to confirm the trend direction. The price being above the MA indicates an uptrend, while below the MA indicates a downtrend.
Background Shading :
The indicator pane is shaded green during uptrend conditions (positive Composite Indicator and price above MA) and red during downtrend conditions (negative Composite Indicator and price below MA).
How Traders Can Use It:
Identifying Trends :
Traders can use the AFHI to identify current market trends. The background shading in the indicator pane provides a visual cue for trend direction, with green indicating an uptrend and red indicating a downtrend.
Trend Confirmation :
The Composite Indicator line, plotted in purple, helps confirm the trend. Positive values suggest a strong uptrend, while negative values indicate a strong downtrend.
Entry and Exit Signals :
Traders can use the transitions of the Composite Indicator and the background shading to time their entry and exit points. For instance, a shift from red to green shading suggests a potential buy opportunity, while a shift from green to red suggests a potential sell opportunity.
Alerts :
The script includes alert conditions that can notify traders when the Composite Indicator signals a new trend direction. Alerts can be set up for both uptrends and downtrends, helping traders stay informed of key market changes.
Strategy Development :
By integrating AFHI into their trading strategies, traders can develop more robust systems that account for market complexity and persistence. The indicator can be used alongside other technical tools to enhance decision-making and improve trade accuracy.

# Fractaldimension

GKD-C Fractal-Dimension-Adaptive SMA w/ DSL [Loxx]Giga Kaleidoscope GKD-C Fractal-Dimension-Adaptive SMA w/ DSL is a Confirmation module included in Loxx's "Giga Kaleidoscope Modularized Trading System".
█ Giga Kaleidoscope Modularized Trading System
What is Loxx's "Giga Kaleidoscope Modularized Trading System"?
The Giga Kaleidoscope Modularized Trading System is a trading system built on the philosophy of the NNFX (No Nonsense Forex) algorithmic trading.
What is the NNFX algorithmic trading strategy?
The NNFX (No-Nonsense Forex) trading system is a comprehensive approach to Forex trading that is designed to simplify the process and remove the confusion and complexity that often surrounds trading. The system was developed by a Forex trader who goes by the pseudonym "VP" and has gained a significant following in the Forex community.
The NNFX trading system is based on a set of rules and guidelines that help traders make objective and informed decisions. These rules cover all aspects of trading, including market analysis, trade entry, stop loss placement, and trade management.
Here are the main components of the NNFX trading system:
1. Trading Philosophy: The NNFX trading system is based on the idea that successful trading requires a comprehensive understanding of the market, objective analysis, and strict risk management. The system aims to remove subjective elements from trading and focuses on objective rules and guidelines.
2. Technical Analysis: The NNFX trading system relies heavily on technical analysis and uses a range of indicators to identify high-probability trading opportunities. The system uses a combination of trend-following and mean-reverting strategies to identify trades.
3. Market Structure: The NNFX trading system emphasizes the importance of understanding the market structure, including price action, support and resistance levels, and market cycles. The system uses a range of tools to identify the market structure, including trend lines, channels, and moving averages.
4. Trade Entry: The NNFX trading system has strict rules for trade entry. The system uses a combination of technical indicators to identify high-probability trades, and traders must meet specific criteria to enter a trade.
5. Stop Loss Placement: The NNFX trading system places a significant emphasis on risk management and requires traders to place a stop loss order on every trade. The system uses a combination of technical analysis and market structure to determine the appropriate stop loss level.
6. Trade Management: The NNFX trading system has specific rules for managing open trades. The system aims to minimize risk and maximize profit by using a combination of trailing stops, take profit levels, and position sizing.
Overall, the NNFX trading system is designed to be a straightforward and easy-to-follow approach to Forex trading that can be applied by traders of all skill levels.
Core components of an NNFX algorithmic trading strategy
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:
1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted
What is Volatility in the NNFX trading system?
In the NNFX (No Nonsense Forex) trading system, ATR (Average True Range) is typically used to measure the volatility of an asset. It is used as a part of the system to help determine the appropriate stop loss and take profit levels for a trade. ATR is calculated by taking the average of the true range values over a specified period.
True range is calculated as the maximum of the following values:
-Current high minus the current low
-Absolute value of the current high minus the previous close
-Absolute value of the current low minus the previous close
ATR is a dynamic indicator that changes with changes in volatility. As volatility increases, the value of ATR increases, and as volatility decreases, the value of ATR decreases. By using ATR in NNFX system, traders can adjust their stop loss and take profit levels according to the volatility of the asset being traded. This helps to ensure that the trade is given enough room to move, while also minimizing potential losses.
Other types of volatility include True Range Double (TRD), Close-to-Close, and Garman-Klass
What is a Baseline indicator?
The baseline is essentially a moving average, and is used to determine the overall direction of the market.
The baseline in the NNFX system is used to filter out trades that are not in line with the long-term trend of the market. The baseline is plotted on the chart along with other indicators, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR).
Trades are only taken when the price is in the same direction as the baseline. For example, if the baseline is sloping upwards, only long trades are taken, and if the baseline is sloping downwards, only short trades are taken. This approach helps to ensure that trades are in line with the overall trend of the market, and reduces the risk of entering trades that are likely to fail.
By using a baseline in the NNFX system, traders can have a clear reference point for determining the overall trend of the market, and can make more informed trading decisions. The baseline helps to filter out noise and false signals, and ensures that trades are taken in the direction of the long-term trend.
What is a Confirmation indicator?
Confirmation indicators are technical indicators that are used to confirm the signals generated by primary indicators. Primary indicators are the core indicators used in the NNFX system, such as the Average True Range (ATR), the Moving Average (MA), and the Relative Strength Index (RSI).
The purpose of the confirmation indicators is to reduce false signals and improve the accuracy of the trading system. They are designed to confirm the signals generated by the primary indicators by providing additional information about the strength and direction of the trend.
Some examples of confirmation indicators that may be used in the NNFX system include the Bollinger Bands, the MACD (Moving Average Convergence Divergence), and the Stochastic Oscillator. These indicators can provide information about the volatility, momentum, and trend strength of the market, and can be used to confirm the signals generated by the primary indicators.
In the NNFX system, confirmation indicators are used in combination with primary indicators and other filters to create a trading system that is robust and reliable. By using multiple indicators to confirm trading signals, the system aims to reduce the risk of false signals and improve the overall profitability of the trades.
What is a Continuation indicator?
In the NNFX (No Nonsense Forex) trading system, a continuation indicator is a technical indicator that is used to confirm a current trend and predict that the trend is likely to continue in the same direction. A continuation indicator is typically used in conjunction with other indicators in the system, such as a baseline indicator, to provide a comprehensive trading strategy.
What is a Volatility/Volume indicator?
Volume indicators, such as the On Balance Volume (OBV), the Chaikin Money Flow (CMF), or the Volume Price Trend (VPT), are used to measure the amount of buying and selling activity in a market. They are based on the trading volume of the market, and can provide information about the strength of the trend. In the NNFX system, volume indicators are used to confirm trading signals generated by the Moving Average and the Relative Strength Index. Volatility indicators include Average Direction Index, Waddah Attar, and Volatility Ratio. In the NNFX trading system, volatility is a proxy for volume and vice versa.
By using volume indicators as confirmation tools, the NNFX trading system aims to reduce the risk of false signals and improve the overall profitability of trades. These indicators can provide additional information about the market that is not captured by the primary indicators, and can help traders to make more informed trading decisions. In addition, volume indicators can be used to identify potential changes in market trends and to confirm the strength of price movements.
What is an Exit indicator?
The exit indicator is used in conjunction with other indicators in the system, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR), to provide a comprehensive trading strategy.
The exit indicator in the NNFX system can be any technical indicator that is deemed effective at identifying optimal exit points. Examples of exit indicators that are commonly used include the Parabolic SAR, the Average Directional Index (ADX), and the Chandelier Exit.
The purpose of the exit indicator is to identify when a trend is likely to reverse or when the market conditions have changed, signaling the need to exit a trade. By using an exit indicator, traders can manage their risk and prevent significant losses.
In the NNFX system, the exit indicator is used in conjunction with a stop loss and a take profit order to maximize profits and minimize losses. The stop loss order is used to limit the amount of loss that can be incurred if the trade goes against the trader, while the take profit order is used to lock in profits when the trade is moving in the trader's favor.
Overall, the use of an exit indicator in the NNFX trading system is an important component of a comprehensive trading strategy. It allows traders to manage their risk effectively and improve the profitability of their trades by exiting at the right time.
How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v1.0 system has five types of modules (indicators/strategies). These modules are:
1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)
(additional module types will added in future releases)
Each module interacts with every module by passing data between modules. Data is passed between each module as described below:
GKD-B => GKD-V => GKD-C(1) => GKD-C(2) => GKD-C(Continuation) => GKD-E => GKD-BT
That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.
This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.
What does the application of the GKD trading system look like?
Example trading system:
Backtest: Strategy with 1-3 take profits, trailing stop loss, multiple types of PnL volatility, and 2 backtesting styles
Baseline: Hull Moving Average
Volatility/Volume: Jurik DMX
Confirmation 1: GKD-V Fractal-Dimension-Adaptive SMA w/ DSL as shown on the chart above
Confirmation 2: Williams Percent Range
Continuation: Fisher Transform
Exit: Rex Oscillator
Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD protocol chain.
Giga Kaleidoscope Modularized Trading System Signals (based on the NNFX algorithm)
Standard Entry
1. GKD-C Confirmation 1 Signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior
Continuation Entry
1. Standard Entry, Baseline Entry, or Pullback; entry triggered previously
2. GKD-B Baseline hasn't crossed since entry signal trigger
3. GKD-C Confirmation Continuation Indicator signals
4. GKD-C Confirmation 1 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 2 agrees
1-Candle Rule Standard Entry
1. GKD-C Confirmation 1 signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
1-Candle Rule Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees
PullBack Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is beyond 1.0x Volatility of Baseline
Next Candle:
1. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees
█ GKD-V Fractal-Dimension-Adaptive SMA w/ DSL
Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL is a fractal-dimension-index-adaptive SMA . The SMA is accelerated during a trend and slowed down during a sideways market, so as to avoid false signals. This indicator uses the fractal dimension to compute an ingest period length into the SMA to output the FDASMA.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Requirements
Inputs
Confirmation 1 and Solo Confirmation: GKD-V Volatility / Volume indicator
Confirmation 2: GKD-C Confirmation indicator
Outputs
Confirmation 2 and Solo Confirmation Complex: GKD-E Exit indicator
Confirmation 1: GKD-C Confirmation indicator
Continuation: GKD-E Exit indicator
Solo Confirmation Simple: GKD-BT Backtest strategy
Additional features will be added in future releases.

Fractal-Dimension-Index-Adaptive Trend Cipher Candles [Loxx]Fractal-Dimension-Index-Adaptive Trend Cipher Candles is a candle coloring indicator that shows both trend and trend exhaustion using Fractal Dimension Index Adaptivity. To do this, we first calculate the dynamic period outputs from the FDI algorithm and then we injection those period inputs into a correlation function that correlates price input price to the candle index. The closer the correlation is to 1, the lighter the green color until the color turns yellow, sometimes, indicating upward price exhaustion. The closer the correlation is to -1, the lighter the red color until it reaches Fuchsia color indicating downward price exhaustion. Green means uptrend, red means downtrend, yellow means reversal from uptrend to downtrend, fuchsia means reversal from downtrend to uptrend.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
Included
Loxx's Expanded Source Types
Related indicators:
Adaptive Trend Cipher loxx]
CFB-Adaptive Trend Cipher Candles
Dynamic Zones Polychromatic Momentum Candles
RSI Precision Trend Candles

FDI-Adaptive, Jurik-Filtered, TMA w/ Price Zones [Loxx]FDI-Adaptive, Jurik-Filtered, TMA w/ Price Zones is a Triangular Moving Average that is Fractal Dimension Index Adaptive with Jurik Smoothing. You'll notice that this combination not only smooths out the signal but also catches bottoms better than other FIR digital filters. This is a multi-layered adaptive moving average. Price zones are calculated using a weighted range function. Future updates will included signals associated with these range bands. For now, however, these range bands serve as support and resistance, stop-loss or take profit, or indicators of market reversal.
What is the Triangular Moving Average
The Triangular Moving Average is basically a double-smoothed Simple Moving Average that gives more weight to the middle section of the data interval. The TMA has a significant lag to current prices and is not well-suited to fast moving markets. TMA = SUM ( SMA values)/ N Where N = the number of periods.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What is Jurik Volty used in the Juirk Filter?
One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive.
What is the Jurik Moving Average?
Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines.
Included:
Bar coloring
Signals
Alerts

FDI-Adaptive Supertrend w/ Floating Levels [Loxx]FDI-Adaptive Supertrend w/ Floating Levels is a Fractal Dimension Index adaptive Supertrend indicator. This allows Supertrend to better adaptive to volatility of the market. This also includes floating levels that act as support and resistance, stop loss or take profit, or indication of market reversal. Additional signal types will be added in the future based on these floating levels.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What is the Supertrend?
Supertrend indicator was created by Olivier Seban to work on different time frames. It works for futures , forex, and equities. It is used in 15 minutes, hourly, weekly, and daily charts . Based on the parameters of multiplier and period, the indicator normally uses 3 for multiplier and 7 for the ATR period as default values. Average True Range is represented by the number of days while the multiplier is the value by which the range is multiplied.
Included:
Bar coloring
Alerts
Signals

FDI-Adaptive Fisher Transform [Loxx]FDI-Adaptive Fisher Transform is a Fractal Dimension Adaptive Fisher Transform indicator.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What is Fisher Transform?
The Fisher Transform is a technical indicator created by John F. Ehlers that converts prices into a Gaussian normal distribution.
The indicator highlights when prices have moved to an extreme, based on recent prices. This may help in spotting turning points in the price of an asset. It also helps show the trend and isolate the price waves within a trend.
Included:
Zero-line and signal cross options for bar coloring
Customizable overbought/oversold thresh-holds
Alerts
Signals

End-pointed SSA of FDASMA [Loxx]End-pointed SSA of FDASMA is a modification of Fractal-Dimension-Adaptive SMA (FDASMA) using End-Pointed Singular Spectrum Analysis. This is a multilayer adaptive indicator.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
See here for more info:
Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL
What is Singular Spectrum Analysis ( SSA )?
Singular spectrum analysis ( SSA ) is a technique of time series analysis and forecasting. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA aims at decomposing the original series into a sum of a small number of interpretable components such as a slowly varying trend, oscillatory components and a ‘structureless’ noise. It is based on the singular value decomposition ( SVD ) of a specific matrix constructed upon the time series. Neither a parametric model nor stationarity-type conditions have to be assumed for the time series. This makes SSA a model-free method and hence enables SSA to have a very wide range of applicability.
For our purposes here, we are only concerned with the "Caterpillar" SSA . This methodology was developed in the former Soviet Union independently (the ‘iron curtain effect’) of the mainstream SSA . The main difference between the main-stream SSA and the "Caterpillar" SSA is not in the algorithmic details but rather in the assumptions and in the emphasis in the study of SSA properties. To apply the mainstream SSA , one often needs to assume some kind of stationarity of the time series and think in terms of the "signal plus noise" model (where the noise is often assumed to be ‘red’). In the "Caterpillar" SSA , the main methodological stress is on separability (of one component of the series from another one) and neither the assumption of stationarity nor the model in the form "signal plus noise" are required.
"Caterpillar" SSA
The basic "Caterpillar" SSA algorithm for analyzing one-dimensional time series consists of:
Transformation of the one-dimensional time series to the trajectory matrix by means of a delay procedure (this gives the name to the whole technique);
Singular Value Decomposition of the trajectory matrix;
Reconstruction of the original time series based on a number of selected eigenvectors.
This decomposition initializes forecasting procedures for both the original time series and its components. The method can be naturally extended to multidimensional time series and to image processing.
The method is a powerful and useful tool of time series analysis in meteorology, hydrology, geophysics, climatology and, according to our experience, in economics, biology, physics, medicine and other sciences; that is, where short and long, one-dimensional and multidimensional, stationary and non-stationary, almost deterministic and noisy time series are to be analyzed.
Included:
Bar coloring
Alerts
Signals
Loxx's Expanded Source Types

Fractal Dimension Index Adaptive Period [Loxx]Fractal Dimension Index Adaptive Period is the adaptive period out of Fractal Dimension Index Adaptivity. This isn't an indicator that shows a signal, instead, it's to be used as auxiliary support and an educational tool to create other indicators. This value can be injected into other indicators to make those indicators Fractal Dimension Index Adaptive.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
Included
Loxx's Expanded Source Types

Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL [Loxx]Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL is a fractal-dimension-index-adaptive SMA. The SMA is accelerated during a trend and slowed down during a sideways market, so as to avoid false signals. This indicator uses the fractal dimension to compute an ingest period length into the SMA to output the FDASMA.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included
2 Signal types
Alerts
Loxx's Expanded Source Types
Bar coloring

Fractal Trend Trading System [DW]This is an advanced utility that uses fractal dimension and trend information to generate useful insights about price activity and potential trade signals.
In this script, my Advanced FDI algorithm is used to estimate the fractal dimension of the dataset over a user defined period.
Fractal dimension, unlike spatial or topological dimension, measures how complexity or detail in an "object" changes as its unit of measurement changes, rather than the number of axes it occupies.
Many forms of time series data (seismic data, ECG data, financial data, etc.) have been theoretically shown to have limited fractal properties.
Consequently, we can estimate the fractal dimension from this data to get an approximate measure of how rough or convoluted the data stream is.
Financial data's fractal dimension is limited to between 1 and 2, so it can also be used to roughly approximate the Hurst Exponent by the relationship H = 2 - D.
When D=1.5, data statistically behaves like a random walk. D above 1.5 can be considered more rough or "mean reverting" due to the increase in complexity of the series.
D below 1.5 can be considered more prone to trending due to the decrease in complexity of the series.
In this script, you are given the option to apply my Band Shelf EQ algorithm to the dataset before estimating dimension.
This enables you to transform your data and observe how its newly measured complexity changes the outputs.
Whether you want to give emphasis to some frequencies, isolate specific bands, or completely alter the shape of your waveform, EQ filtration makes for an interesting experience.
The default EQ preset in this script removes the low shelf, then attenuates low end and high end oscillations.
The dominant cyclical components (bands 3 - 5 on default settings) are passed at 100%, keeping emphasis on 8 to 64 sample per cycle oscillations.
The estimated dimension is then used to calculate the High Dimension Zone and the Error Bands.
Both of these components are great for analyzing trends and for estimating support and resistance values.
The High Dimension Zone is composed of a high line, low line, and midline that update their values when D is at or above the user defined zone activation threshold.
The zone is then averaged over a user defined amount of updates and zone width is multiplied by a user defined value.
The Error Bands are composed of a high, low, and middle band that are calculated using an error adjusted adaptive filter algorithm that utilizes dimension as the smoothing constant modulator.
The basis filter for the error bands has two calculation types built in:
-> MA - Calculates the filters as adaptive moving averages modulated by D.
-> WAP - Calculates the filters as adaptive weighted average prices modulated by D.
The WAP starting point can be based on the High Dimension Zone being moved or a user defined interval.
You can also define the WAP's minimum and maximum periods for additional control of the initial and decayed sensitivity states.
The alpha (smoothing constant) modulator can be fine tuned using the designated dimension thresholds.
When D is at or below the low dimension threshold, the filter is most responsive, and vice-versa for the high dimension threshold.
Alpha is then multiplied by a user defined amount for additional control of sensitivity.
Band width is then multiplied by a user defined value.
A Hull transformation can be optionally performed on the zone averaging and band filter algorithms as well, which will alter the frequency and phase responses at the cost of some overshoot.
This transformation is the same as a typical Hull equation, but with custom filters being used instead of WMA.
The calculated outputs are then used to gauge the trend for signal and color scheme calculations.
First, a dominant trend indication is selected from its designated dropdown tab.
The available built in indications to choose from are:
-> Band Trend (Outer) - Detects band breakouts and saves their direction to gauge trend.
-> Band Trend (Median) - Uses disparity between source and the band median to gauge trend.
-> Zone Trend (Expansion) - Detects when the high fractal zone expands and saves its direction to gauge trend.
-> Zone Trend (Outer Levels) - Detects zone breakouts and saves their direction to gauge trend.
-> Zone Trend (Median) - Uses disparity between source and the zone median to gauge trend.
Then the trend output is optionally filtered before triggering signals.
There are multiple trend filtration options built into this script that can be used individually or in unison:
-> Filter Trend With High Fractal Zone - Filters the trend using the specified zone level or combination of levels with either disparity or crossover conditions.
There is a set of options for bullish and bearish trends.
-> Filter Trend With Error Bands - Filters the trend using the specified band level or combination of levels with either disparity or crossover conditions.
There is a set of options for bullish and bearish trends.
-> Filter Trend With Band - Zone Disparity Condition - Filters the trend using the specified band level, zone level, and disparity direction.
There is a set of options for bullish and bearish trends.
-> Filter By Zone That Moves With The Trend - Filters the specified trend by detecting when the high fractal zone’s direction correlates.
-> Filter By Bands That Move With The Trend - Filters the specified trend by detecting when the error bands’ direction correlates.
-> Filter Using Wave Confirmation - Filters the specified trend by detecting when source is in a correlating wave with user defined length.
You can also choose separate lengths for bullish and bearish trends.
-> Filter By Bars With Decreasing Dimension - Filters the specified trend by detecting when fractal dimension is decreasing, suggesting source is approaching more linear movement.
The filtered trend output is then used to generate entry and exit signals.
There are multiple options included to fine tune how these signals behave.
For entries, you have the following options built in:
-> Limit Entry Dimension - Limits the range of dimensional values that are acceptable for entry with user defined thresholds.
This can be incredibly useful for filtering out entries taken when price is moving in a more complex pattern,
or when price is approaching a peak and you’re a little late to the party.
-> Enable Position Increase Signals - Enables more entry signals to fire up to a user defined number of times when a position is active.
This is helpful for those who incrementally increase their positions, or for those who want to see additional signals as reference.
-> Limit Number Of Consecutive Trades - Limits the number of consecutive trades that can be opened in a single direction to a user defined maximum.
This is especially useful for markets that only trend for brief durations.
By limiting the amount of trades you take in one direction, you have more control over your market exposure.
There is a set of these options for both bullish and bearish entries.
For exits, you have the following options built in:
-> Include Exit Signals From High Fractal Zone - Enables exit signals generated from either crossover or disparity conditions between price and a specified zone level.
-> Include Exit Signals From Error Bands - Enables exit signals generated from either crossover or disparity conditions between price and a specified zone level.
-> Include Inactive Trend Output For Exits - Triggers exit signals when the filtered trend output is an inactive value.
-> Dimension Target Exit Method - Triggers exit signals based on fractal dimension hitting a user defined threshold.
You can either choose for the exit to trigger instantly, or after dimension reverts from the target by a user specified amount.
-> Exit At Maximum Entry Dimension - Triggers exit signals when dimension exceeds the maximum entry limit.
-> Number Of Signals Required For 100% Exit - Controls the number of exit signals required to close the position.
You can also choose whether or not to include partial exits.
Enabling them will fire a partial signal when an exit occurs, but the position is not 100% closed.
Of course, there is a set of these options for bullish and bearish exits.
In my opinion, no system is complete without some sort of risk management protocol in place.
So in this script, bullish and bearish trades come equipped with optional protective SL and TP levels with signals.
The levels can be fixed or trailing, and are calculated with a user defined scale.
The available scales for SL and TP distances are ticks, pips, points, % of price, ATR, band range, zone range, or absolute numerical value.
Now what if you have some awesome signals of your own that you’d like to use in conjunction with this script?
Well good news. You can!
In addition to all of the customizable features built into the script, you can integrate your own signals into the system using the external data inputs and linking your script.
This adds a whole new layer of customization to the system.
With external signals, you can use your own custom dominant trend indication, filter the dominant trend, and trigger exits and protective stops using custom signals.
The signal input is an integer format. 1=Bull Signal, -1=Bear Signal, 2=Bull Exit, -2=Bear Exit, 3=Bull SL Hit, -3=Bear SL Hit, 4=Bull TP Hit, -4=Bear TP Hit.
You can also use the external input as a custom source value for either dimension or global sources to further tailor the system to your liking.
The color scheme in this script utilizes two custom gradients that can be chosen for bar and background colors:
-> Trend (Dominant or Filtered) - A polarized gradient that shows green scaled values for bullish trend and red scaled values for bearish trend.
The colors are brighter and more vibrant as perceived trend strength increases.
-> Dimension - A thermal gradient that shows cooler colors when dimension is higher, and hotter colors when dimension is lower.
Both color schemes are dependent on the designated dimension thresholds.
The script comes equipped with alerts for entries, additional entries, exits, partial exits, and protective stops so you can automate more and stare at your charts less.
And lastly, the script comes equipped with additional external outputs to further your analysis:
-> Entry And Exit Signals - Outputs in the same format as the external signal input with these additions: 5=Bull Increase, -5=Bear Increase, 6=Bull Reduce, -6=Bear Reduce.
You can use these to send to other scripts, including strategy types so you can backtest your performance on TV’s engine.
-> Dominant Trend - Outputs 1 for bullish and -1 for bearish. Can be used to send trend signals to another script.
I designed this tool with individuality in mind.
Every trader has a different situation. We trade on different schedules, markets, perspectives, etc.
Analytical systems of basically any type are very seldom (if ever) “one size fits all” and usually require a fair amount of modification to achieve desirable results.
That’s why this system is so freely customizable.
Your system should be flexible enough to be tailored to your analytical style, not the other way around.
When a system is limited in what you can control, it limits your experience, analytical potential, and possibly even profitability.
This is not your typical pre-set system. If you're looking for just another "buy, sell" script that requires minimal thought, look elsewhere.
If you’re ready to dive into a powerful technical system that allows you to tailor the experience to your style, welcome!
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This is a premium script, and access is granted on an invite-only basis.
To gain access, get a copy of the system overview, or for additional inquiries, send me a direct message.
I look forward to hearing from you!
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General Disclaimer:
Trading stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument has large potential rewards, but also large potential risk.
You must be aware of the risks and be willing to accept them in order to invest in stocks, futures, Forex, options, ETFs or cryptocurrencies.
Don’t trade with money you can’t afford to lose.
This is neither a solicitation nor an offer to Buy/Sell stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument.
No representation is being made that any account will or is likely to achieve profits or losses of any kind.
The past performance of any trading system or methodology is not necessarily indicative of future results.

Advanced Fractal Dimension Index [DW]This is an experimental study based on Benoit Mandelbrot's fractal dimension concepts.
Fractal dimension is a ratio providing a statistical measure of complexity comparing how detail in a pattern changes with the scale at which it's measured.
The concept of a fractional or fractal dimension was derived from an unconventional approach to standard geometric definitions.
We all know the standard geometric rules of dimension: D=0 is a point, D=1 is a line, D=2 is a plane, and D=3 is a volume, based on the number of axes being occupied.
However, by taking a fractal geometric approach, we can define dimension like so:
N = s^-D , where N is the number of measurement segments, s is the scale factor, and D is the dimension of the object being measured.
This approach typifies conventional knowledge of dimensions as well. Here are some basic examples:
If we divide a line segment into 4 equal line segments, then we'd get 4 = (1/4)^-D. Solving for D, we get D=1, which is what we'd expect from a line.
If we divide a square into 16 equal squares, we'd be separating each line on the square into 4 pieces, so 16 = (1/4)^-D. Solving for D, we get D=2, which is what we'd expect from a square.
If we divide a cube into 64 equal cubes, we'd be separating each line on the cube into 4 pieces, so 64 = (1/4)^-D. Solving for D, we get D=3, which is what we'd expect from a cube.
The same approach can be applied to fractal objects, although admittedly it's less intuitive.
Let's say you use a stick to measure a curve, then you divide the stick into 3 equal segments and re-measure the length.
But rather than the re-measured curve showing a length of 3 of the smaller segments, it is actually 4 segments long.
This irregularity means that detail has increased as you scaled your measurement down, so the curve is dimensionally higher than the space it resides in.
In this example: 4 = (1/3)^-D. Solving for D, we get D=1.2619.
For a true fractal, this scaling of self-similar measurements would continue infinitely.
However, unlike true fractals, most real world phenomena exhibit limited fractal properties, in which they can be scaled down to some limited quantity.
Many forms of time series data (seismic data, ECG data, financial data, etc.) have been theoretically shown to have limited fractal properties.
Consequently, we can estimate fractal dimension from this data to get an approximate measure of how rough or convoluted the data stream is.
Financial data's fractal dimension is limited to between 1 and 2, so it can be used to roughly approximate the Hurst Exponent by the relationship H = 2 - D.
When D=1.5, data statistically behaves like a random walk. D above 1.5 can be considered more rough or "mean reverting" due to the increase in complexity of the series.
D below 1.5 can be considered more prone to trending due to the decrease in complexity of the series.
In this study, you are given the option to apply equalization (EQ) to the dataset before estimating dimension.
This enables you to transform your data and observe how its complexity changes as well.
Whether you want to give emphasis to some frequencies, isolate specific bands, or completely alter the shape of your waveform, EQ filtration makes for an interesting experience.
The default EQ preset in this script removes the low shelf, then attenuates low end and high end oscillations.
The dominant cyclical components (bands 3 - 5 on default settings) are passed at 100%, keeping emphasis on 8 to 64 sample per cycle oscillations.
In addition, if you're wanting a simpler filter process, or if you want a little extra, there are options included to pre and post smooth the data with 2 pole Butterworth LPFs.
The dimension estimation in this script works by measuring changes in detail using source's maximum range over a given lookback length.
In essence, it recursively updates its length parameter based on changes in range compared to the maximum over the lookback period, then uses the data to solve for D.
The FDI algorithm works on any length greater than 1. However, I didn't notice any particularly meaningful results with lookback lengths of 15 or less.
A custom color scheme is included in this script as well for FDI fill and bar colors.
The color scheme in this script is a multicolored thermal styled gradient.
The scale of gradient values is determined by the designated high and low dimension thresholds. These thresholds determine what range of values the gradient will focus on.
Values at the high threshold are the coolest and darkest, and values at the low threshold are the warmest and brightest.
Basically, the "trendier" the data is, the brighter and warmer the color will be.
Signals and alerts are included as well for crossovers on the high and low dimension thresholds.
These signals can also be externally linked to another script.
The output format is 1 for the trigger, and 0 otherwise. Basic boolean logic.
To integrate these signals with your script, simply use a source input and select the signal output from this script that you wish to use from the dropdown menu.
Fractal dimension is a powerful tool that can give valuable insight about the complexity and persistence / anti-persistence of price movements.
When used in conjunction with other analytical methods, it can prove to be a surprisingly beneficial tool to have in the arsenal.
-----------------------------------------------------
This is a premium script, and access is granted on an invite-only basis.
To gain access, get a copy of the indicator overview, or for additional inquiries, send me a direct message.
I look forward to hearing from you!
-----------------------------------------------------
General Disclaimer:
Trading stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument has large potential rewards, but also large potential risk.
You must be aware of the risks and be willing to accept them in order to invest in stocks, futures, Forex, options, ETFs or cryptocurrencies.
Don’t trade with money you can’t afford to lose.
This is neither a solicitation nor an offer to Buy/Sell stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument.
No representation is being made that any account will or is likely to achieve profits or losses of any kind.
The past performance of any trading system or methodology is not necessarily indicative of future results.