Permutation Entropy Complexity OscillatorPermutation Entropy — Complexity Oscillator
What this script does
This is a complexity oscillator: it measures, on a 0–1 scale, how random versus structured recent price action is — not which direction price is going, but whether there is any exploitable order to go on. It reads the order of successive moves (not their size): every three consecutive prices form one of six up/down shapes ("ordinal patterns"), and the oscillator measures how evenly those shapes are spread over a rolling window. Near 1, all shapes are equally likely — the tape is effectively random. Near 0, a few shapes dominate — the tape is structured and, in principle, more predictable.
Why these components are combined (mashup justification)
This is not several indicators shown side by side. There is exactly one plotted value — the normalized ordinal-pattern entropy — and every other element is a decision-support layer built on that single value:
The entropy engine is the core. Conventional price-level oscillators tell you where price is in its range; none of them tell you whether the range is even worth trading. Ordinal-pattern entropy is amplitude-free and noise-robust, so it isolates one orthogonal question — is there structure right now? — that the price-level family cannot answer.
The predictable / random thresholds classify the reading into a regime (structured / mixed / random). They don't add a second indicator; they interpret the one oscillator.
The statistical-complexity measure (complexity–entropy plane) is computed from the same ordinal-pattern counts and answers the question entropy cannot: low entropy alone can be genuinely structured or trivially degenerate (near-periodic). Pairing entropy with complexity separates "richly structured and potentially exploitable" from "low-entropy but trivial," so a signal only treats the tape as structured when both agree.
The momentum sign does nothing on its own — it only sets the direction of an already-armed regime signal. The bet is "a structured tape tends to keep doing what it's doing"; momentum just says which way that is.
The calibration harness is the reason the rest is trustworthy. It logs every signal the oscillator arms and, a fixed horizon later, checks whether price actually extended ≥ k×ATR in that direction — then reports Hit %, the unconditional Base %, and the Edge (Hit − Base).
Every part answers one question about the same entropy reading, which is why they belong in one script rather than as separate studies.
What makes it original
Two things. First, it brings an information-theoretic structure measure — usually seen only in research, not on charts — into a live, bounded oscillator with regime bands and a clean visual. Second, and more importantly, it does not assume the common claim that "low entropy means predictable, tradeable price." It tests that claim, live, on your instrument, with the built-in calibration harness. If low-entropy signals don't actually precede a forward move on your symbol and timeframe, the Edge row shows it plainly — often at or below zero. That honesty layer, not the entropy calculation alone, is the contribution.
How to use it
Add to a chart. Defaults target intraday index futures (e.g. NSE NIFTY); for other markets simply change the chart, or set the Price source input (group 01) — you can even feed it another indicator's output.
Read the regime at a glance from the background tint: green = genuine structure (low entropy and high complexity → the actionable state), amber = low-complexity / trivial low entropy (caution), grey = random / efficient tape (stand aside), no tint = mixed (wait). The line carries the same colour, with a bright line confirming genuine structure; the dashboard "Tape (plane)" chip shows the same state in words.
Optionally enable the statistical-complexity overlay (group 05) to see the complexity–entropy plane directly: it peaks at intermediate entropy where structure is richest and falls toward zero for both pure noise and trivial tapes. The dashboard shows the live complexity value and a ● when it clears the genuine-structure threshold.
Tie-robustness and delay τ (group 02): on discrete / tick-quantised instruments (index futures, where equal consecutive prints are common) equal values bias ordinal-pattern entropy toward false structure. The tie-robust dither (on by default) and an optional delay τ > 1 mitigate this; τ also probes a coarser timescale. Set τ = 1 and tie-robust off to reproduce the plain estimator.
Triangles mark the moment a predictable regime starts, with direction set by recent momentum — points to investigate, not automatic entries. With the complexity gate on (default), a signal only arms when complexity also confirms genuine structure; turn it off to A/B that choice against the entropy-only signal in the Edge row.
Read the Edge row before trusting the signal. A positive Edge means structured starts preceded a forward move more often than chance here; near or below zero means low entropy is not buying you predictability on this instrument.
Window length, smoothing, embedding delay, the two entropy thresholds, the complexity threshold, the momentum length, and the calibration horizon / threshold are all configurable.
Limitations
Entropy describes the tape's structure, not its direction — low entropy can precede a clean trend or a clean oscillation. The momentum-direction bet is one testable interpretation, not a law; the calibration row is there precisely so you don't take it on faith.
Statistics are in-sample, close-to-close, without costs — a study aid, not a backtest.
The reading needs a full window before it is meaningful (the panel shows "warm" until then).
This is an analytical complexity study. It issues no automated buy/sell instructions and is not a strategy.
Concept credit
Permutation entropy / ordinal-pattern analysis — Christoph Bandt and Bernd Pompe (2002).
Information entropy — Claude E. Shannon (1948).
Statistical complexity (the complexity–entropy plane) — the MPR statistical-complexity measure of P. W. Lamberti, M. T. Martín, A. Plastino and O. A. Rosso, applied to markets via the complexity–entropy causality plane of L. Zunino, M. Zanin, B. M. Tabak, D. G. Pérez and O. A. Rosso (2010).
Tie / equal-value bias in ordinal patterns — informed by the work of D. Cuesta-Frau and colleagues (2018).
The implementation, the regime/threshold logic, the complexity gate, the tie-robust dither, the calibration harness and the packaging are original.
Disclaimer
For research and educational purposes only. This script is not financial advice, not a recommendation, and not a guarantee of future results. Indicators describe price behaviour; they do not predict the future. Trading carries risk of loss. Test on out-of-sample data and make your own decisions. The author accepts no liability for any use of this script. Indicator
[GYTS-CE] Pattern Texture Codex (PTC)Pattern Texture Codex (Community Edition)
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is the Pattern Texture Codex?
Standard technical analysis focuses on two dimensions: Amplitude (how far price moves) and Momentum (how fast price moves). The Pattern Texture Codex introduces a third: Structure (how price moves).
This indicator implements Permutation Entropy (PE), a complexity measure from dynamical systems theory that captures whether price evolves in structured patterns or chaotic noise. We call this "Market Texture":
🫧 Smooth Texture (Low Entropy): Price evolves in ordered, predictable patterns. Trends are durable and causality is high. Momentum strategies favoured.
🌵 Rough Texture (High Entropy): Price evolves chaotically. The market is noisy, trends are fragile. Mean reversion or defensive sizing recommended.
💮 Why Use This Indicator?
Most "entropy" indicators on PulseWire fall into common traps:
Shannon entropy of price histograms — measures value distribution but ignores temporal sequence
Approximate Entropy (ApEn) — measures amplitude similarity with O(N²) computational cost
Volatility metrics labelled "entropy" — captures magnitude, not pattern structure
Mathematical errors — normalised values that don't form valid probability distributions
The Pattern Texture Codex provides true ordinal pattern analysis — it examines the sequence of price movements, not just their distribution or magnitude. A smooth uptrend and choppy consolidation may have identical volatility, but their texture is completely different.
↑ Pattern Texture Codex with dynamic threshold bands. Rough Texture (high entropy) often indicates reversals, while Smooth Texture (low entropy) often precedes trend continuation.
🌸 --------- HOW IT WORKS --------- 🌸
💮 Core Concept: Ordinal Patterns
Instead of analysing raw price values, Permutation Entropy converts price into ordinal patterns — the relative ordering of consecutive data points.
For example, with embedding dimension D=3 (three points per pattern):
Pattern "012": first < second < third → ascending
Pattern "210": first > second > third → descending
Pattern "102": middle value smallest → valley shape
The indicator counts how often each pattern appears over a lookback window, then calculates the Shannon entropy of this distribution.
↑ With D=3, three consecutive data points determine each pattern. Left: ascending pattern "012" (first point smallest, second middle, third greatest). Right: descending pattern "210" (first point greatest, second middle, third smallest).
💮 Calculation Overview
The normalised Permutation Entropy is computed as:
H = −∑ p(π) · ln(p(π)) / ln(D!)
Where:
• p(π) is the probability of each ordinal pattern π
• D is the embedding dimension (number of points per pattern)
• D! is the total possible patterns (e.g., 4! = 24 for D=4)
The result ranges from 0 to 1:
• H → 0 : One pattern dominates — highly structured, predictable
• H → 1 : All patterns equally likely — pure randomness
↑ Full calculation example at D=3 showing the lowest entropy point (green vertical line). With 3!=6 possible patterns, the monotonic rising pattern "012" dominates while three other patterns occur only once. The frequency column feeds into the entropy contribution formula, yielding H(3)=1.039. Normalising produces 0.4019 — matching the indicator output exactly.
💮 Theoretical Background
Permutation Entropy has deep theoretical foundations. For piecewise monotone maps, it converges to the Kolmogorov-Sinai entropy — the fundamental measure of chaos in dynamical systems.
Key scientific properties:
• Scale invariance — analyses rank orderings, invariant to monotonic transformations
• Noise robustness — ordinal encoding naturally filters high-frequency noise
• Computational efficiency — O(1) amortised per bar with lookup acceleration
• Micro-structure sensitivity — captures specific sequence patterns, not just distribution
🌸 --------- KEY FEATURES --------- 🌸
💮 Lookup Table Acceleration
Standard PE requires sorting each embedding vector — O(D log D) operations per bar. This implementation uses precomputed transition tables from Unakafova & Keller (2013), reducing complexity to O(D) per bar.
The key insight: successive ordinal patterns in overlapping windows share (D−1) data points. Rather than recomputing from scratch, the algorithm derives the new pattern from the previous one using a single table lookup.
Enabled by default for Delay=1 and Dimension ∈ {3, 4, 5}
Falls back to standard calculation for D=2, D=6
💮 Flexible Threshold Modes
The indicator supports four independent threshold modes for both Smooth and Rough detection:
Static — Fixed threshold values you define
Dynamic — Adaptive bands based on entropy baseline ± standard deviation
Percentile — Threshold at Nth percentile of recent entropy history
Disabled — No threshold for that direction
You can mix modes: for example, Dynamic for Smooth detection while using Percentile for Rough detection.
🌸 --------- CONFIGURATION --------- 🌸
💮 General Settings
• Source — Price series to analyse (default: close)
• Smoothing Critical Period — Smoothing via 2-pole Ultimate Smoother (default: 0 = disabled). Reveals underlying texture by filtering entropy noise.
💮 Entropy Calculation
Dimension (D) — Points per ordinal pattern:
• D=3: 6 patterns — fast, stable. Good for limited lookback.
• D=4: 24 patterns — balanced, captures V-reversals. Recommended.
• D=5: 120 patterns — sensitive, captures W/M patterns. Noisier.
• D=6: 720 patterns — maximum sensitivity. No lookup acceleration.
Lookback — Estimation window size. Hard minimum: D × 5. Statistical recommendation: 5 × D! (e.g., 120 for D=4). Default: 100.
Delay (τ) — Stride between points in each pattern (default: 1). Change only for oversampled data.
Lookup Acceleration — Enables transition tables for D ∈ {3, 4, 5} with Delay=1.
💮 Threshold Management
Rough/Smooth Mode — Static, Dynamic, Percentile, or Disabled for each threshold
Static Values — Fixed threshold when Static mode selected
Std Dev Multiplier — Band width for Dynamic mode (default: 2.0σ)
Baseline/Deviation Length — Lookback for Dynamic mode calculations
Percentile Settings — Lookback and percentile values for Percentile mode
💮 Visualisation & Alerts
Palette — Colour scheme (default: GYTS Purple)
Colouring Bars — Applies texture colours to chart candles
Dark Mode — Optimises colour intensity for dark backgrounds
Alerts — Triggers when entropy crosses above/below thresholds
🌸 --------- USAGE GUIDE --------- 🌸
💮 Getting Started
Apply the indicator with default settings:
• Dimension: 4 (balanced complexity, captures V-shaped reversals)
• Lookback: 100 (responsive; statistical ideal: ≥120 for 5× coverage)
• Smooth Threshold: Dynamic mode with 2.0σ multiplier
Observe how entropy rises during choppy consolidation and falls during clean trends.
💮 Interpretation
Entropy Value (0 to 1):
Below 0.6: Strong pattern dominance — highly ordered
0.7–0.9: Normal complexity — typical market behaviour
Above 0.95: Near-random — patterns uniformly distributed
Transitions:
Watch for regime changes. When entropy rises sharply after a prolonged smooth period, the trend may be losing coherence. When entropy falls from elevated levels, a new trend may be establishing.
↑ Texture transitions during a trend-to-consolidation regime change. During the uptrend, similar patterns (D=3) recur frequently and entropy decreases. As the market transitions to consolidation, entropy rises — signalling the trend is losing structure.
💮 Trading Applications
Trend Filtering — Only take trend-following signals during Smooth texture.
Mean Reversion Timing — Elevated entropy often precedes mean reversion.
Position Sizing — Reduce exposure during Rough texture.
Exit Management — Tighten stops when entropy rises during a position.
💮 Integration with GYTS Suite
The Pattern Texture Codex exports two signals:
PE Continuous — Raw entropy value (0 to 1)
PE Ternary — State signal (+1 = Rough, 0 = Neutral, −1 = Smooth)
These can be read by Flux Composer or used as filter conditions with Market Regime Detector .
🌸 --------- PARAMETER TUNING --------- 🌸
💮 Lookback Selection
Shorter lookbacks react faster but may produce unstable estimates:
50–100: Responsive. Good for intraday regime detection.
100–200: Balanced. Recommended for swing trading.
200–500: Stable. Better for position trading or noisy instruments.
The indicator enforces a hard minimum of D × 5 to prevent meaningless output.
↑ Three dimensions (D=3, D=4, D=5) with their academically recommended minimum lookback periods.
💮 Threshold Tuning
For Smooth Detection:
Dynamic mode with 2.0σ works well across most instruments. Lower multipliers (1.5σ) detect structure earlier but may false-trigger.
For Rough Detection:
Percentile mode at 90th percentile identifies only extreme chaos. Static threshold of 0.95+ focuses on near-random conditions.
Consider disabling Rough detection entirely if your strategy only cares about identifying structured trends.
↑ The three threshold modes on the same PTC calculation. Both upper and lower thresholds are independently configurable.
🌸 --------- LIMITATIONS --------- 🌸
Amplitude Blindness — PE treats all patterns equally regardless of magnitude. A 0.1% drift and a 10% crash produce identical entropy if their ordinal patterns match.
Equal Values (Ties) — Handled via temporal tie-breaking (recent values rank higher), but heavily discretised data may produce edge-case behaviour.
Sample Size Requirements — Very short lookbacks (below D × 5) produce unreliable estimates. Statistical reliability improves with larger samples.
Not Predictive Alone — Low entropy indicates structure exists, not that the trend will continue. Combine with directional analysis for trading decisions.
Lag During Transitions — The sliding window approach introduces inherent lag when market texture changes.
🌸 --------- CREDITS --------- 🌸
💮 Academic Sources
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88 (17), 174102. DOI
Unakafova, V., & Keller, K. (2013). Efficiently measuring complexity on the basis of real-world data. Entropy, 15 (10), 4392-4415. DOI
Ehlers, J. F. (2024). The Ultimate Smoother. Technical Analysis of Stocks & Commodities , 2024-04. TASC
💮 Libraries Used
FiltersToolkit — Ultimate Smoother and other curated filters
PatternTransitionTables — Precomputed lookup tables for O(1) pattern transitions
ColourUtilities — Gradient palette generation and colour management
Indicator
PatternTransitionTablesPatternTransitionTables Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
This library provides precomputed state transition tables to enable ultra-efficient, O(1) computation of Ordinal Patterns. It is designed specifically to support high-performance indicators calculating Permutation Entropy and related complexity measures.
💮 The Problem & Solution
Calculating Permutation Entropy, as introduced by Bandt and Pompe (2002), typically requires computing ordinal patterns within a sliding window at every time step. The standard successive-pattern method (Equations 2+3 in the paper) requires ≤ 4d-1 operations per update.
Unakafova and Keller (2013) demonstrated that successive ordinal patterns "overlap" significantly. By knowing the current pattern index and the relative rank (position l) of just the single new data point, the next pattern index can be determined via a precomputed look-up table. Computing l still requires d comparisons, but the table lookup itself is O(1), eliminating the need for d multiplications and d additions. This reduces total operations from ≤ 4d-1 to ≤ 2d per update (Table 4). This library contains these precomputed tables for orders d = 2 through d = 5.
🌸 --------- 2. THEORETICAL BACKGROUND --------- 🌸
💮 Permutation Entropy
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series.
doi.org
This concept quantifies the complexity of a system by comparing the order of neighbouring values rather than their magnitudes. It is robust against noise and non-linear distortions, making it ideal for financial time series analysis.
💮 Efficient Computation
Unakafova, V. A., & Keller, K. (2013). Efficiently Measuring Complexity on the Basis of Real-World Data.
doi.org
This library implements the transition function φ_d(n, l) described in Equation 5 of the paper. It maps a current pattern index (n) and the position of the new value (l) to the successor pattern, reducing the complexity of updates to constant time O(1).
🌸 --------- 3. LIBRARY FUNCTIONALITY --------- 🌸
💮 Data Structure
The library stores transition matrices as flattened 1D integer arrays. These tables are mathematically rigorous representations of the factorial number system used to enumerate permutations.
💮 Core Function: get_successor()
This is the primary interface for the library for direct pattern updates.
• Input: The current pattern index and the rank position of the incoming price data.
• Process: Routes the request to the specific transition table for the chosen order (d=2 to d=5).
• Output: The integer index of the next ordinal pattern.
💮 Table Access: get_table()
This function returns the entire flattened transition table for a specified dimension. This enables local caching of the table (e.g. in an indicator's init() method), avoiding the overhead of repeated library calls during the calculation loop.
💮 Supported Orders & Terminology
The parameter d is the order of ordinal patterns (following Bandt & Pompe 2002). Each pattern of order d contains (d+1) data points, yielding (d+1)! unique patterns:
• d=2: 3 points → 6 unique patterns, 3 successor positions
• d=3: 4 points → 24 unique patterns, 4 successor positions
• d=4: 5 points → 120 unique patterns, 5 successor positions
• d=5: 6 points → 720 unique patterns, 6 successor positions
Note: d=6 is not implemented. The resulting code size (approx. 191k tokens) exceeds the Pine Script limit of 100k tokens (as of 2025-12). Library
permutation█ OVERVIEW
This library provides functions for generating permutations of string or float arrays, using an iterative approach where pine has no recursion. It supports allowing/limiting duplicate elements and handles large result sets by segmenting them into manageable chunks within custom Data types. The most combinations will vary, but the highest is around 250,000 unique combinations. depending on input array values and output length. it will return nothing if the input count is too low.
█ CONCEPTS
This library addresses two key challenges in Pine Script:
• Recursion Depth Limits: Pine has limitations on recursion depth. This library uses an iterative, stack-based algorithm to generate permutations, avoiding recursive function calls that could exceed these limits.
• Array Size Limits: Pine arrays have size restrictions. This library manages large permutation sets by dividing them into smaller segments stored within a custom Data or DataFloat type, using maps for efficient access.
█ HOW TO USE
1 — Include the Library: Add this library to your script using:
import kaigouthro/permutation/1 as permute
2 — Call the generatePermutations Function:
stringPermutations = permute.generatePermutations(array.from("a", "b", "c"), 2, 1)
floatPermutations = permute.generatePermutations(array.from(1.0, 2.0, 3.0), 2, 1)
• set : The input array of strings or floats.
• size : The desired length of each permutation.
• maxDuplicates (optional): The maximum allowed repetitions of an element within a single permutation. Defaults to 1.
3 — Access the Results: The function returns a Data (for strings) or DataFloat (for floats) object. These objects contain:
• data : An array indicating which segments are present (useful for iterating).
• segments : A map where keys represent segment indices and values are the actual permutation data within that segment.
Example: Accessing Permutations
for in stringPermutations.segments
for in currentSegment.segments
// Access individual permutations within the segment.
permutation = segmennt.data
for item in permutation
// Use the permutation elements...
█ TYPES
• PermutationState / PermutationStateFloat : Internal types used by the iterative algorithm to track the state of permutation generation.
• Data / DataFloat : Custom types to store and manage the generated permutations in segments.
█ NOTES
* The library prioritizes handling potentially large permutation sets. 250,000 i about the highest achievable.
* The segmentation logic ensures that results are accessible even when the total number of permutations exceeds Pine's array size limits.
----
Library "permutation"
This library provides functions for generating permutations of user input arrays containing either strings or floats. It uses an iterative, stack-based approach to handle potentially large sets and avoid recursion limitation. The library supports limiting the number of duplicate elements allowed in each permutation. Results are stored in a custom Data or DataFloat type that uses maps to segment large permutation sets into manageable chunks, addressing Pine Script's array size limitations.
generatePermutations(set, size, maxDuplicates)
> Generates permutations of a given size from a set of strings or floats.
Parameters:
set (array) : (array or array) The set of strings or floats to generate permutations from.
size (int) : (int) The size of the permutations to generate.
maxDuplicates (int) : (int) The maximum number of times an element can be repeated in a permutation.
Returns: (Data or DataFloat) A Data object for strings or a DataFloat object for floats, containing the generated permutations.
stringPermutations = generatePermutations(array.from("a", "b", "c"), 2, 1)
floatPermutations = generatePermutations(array.from(1.0, 2.0, 3.0), 2, 1)
generatePermutations(set, size, maxDuplicates)
Parameters:
set (array)
size (int)
maxDuplicates (int)
PermutationState
PermutationState
Fields:
data (array) : (array) The current permutation being built.
index (series int) : (int) The current index being considered in the set.
depth (series int) : (int) The current depth of the permutation (number of elements).
counts (map) : (map) Map to track the count of each element in the current permutation (for duplicates).
PermutationStateFloat
PermutationStateFloat
Fields:
data (array) : (array) The current permutation being built.
index (series int) : (int) The current index being considered in the set.
depth (series int) : (int) The current depth of the permutation (number of elements).
counts (map) : (map) Map to track the count of each element in the current permutation (for duplicates).
Data
Data
Fields:
data (array) : (array) Array to indicate which segments are present.
segments (map) : (map) Map to store permutation segments. Each segment contains a subset of the generated permutations.
DataFloat
DataFloat
Fields:
data (array) : (array) Array to indicate which segments are present.
segments (map) : (map) Map to store permutation segments. Each segment contains a subset of the generated permutations.
Library
Library
