Isotropic Coordinate System (ICS)Library "ICS"
Isotropic Coordinate System (ICS): a dimensionless price-time space
for scale-invariant chart geometry.
Vertical axis: y = ln(price) / sigma, where sigma is the Yang-Zhang (2000)
minimum-variance, drift-independent, gap-consistent OHLC volatility estimator.
Horizontal axis: two scalings via the XScale enum.
legacy : x = bars / lookback. Linear window fraction. Backward compatible.
isotropic : x = sqrt(bars / lookback), with y additionally divided by
sqrt(lookback). Diffusion-consistent (sqrt-time scaling), so that
tan(theta) equals the z-score of the move and 45 degrees
corresponds to a move of exactly one standard deviation
of the n-bar log-return distribution. Assumes approximately
iid returns within the sigma window (the standard assumption
behind sqrt-time scaling; see Danielsson & Zigrand, 2006, for
its known limits under vol clustering and jumps).
Every output (angle, length, area, centroid) is a pure dimensionless number,
comparable across symbols, currencies, and timeframes.
Reference: Yang, D. & Zhang, Q. (2000), "Drift-Independent Volatility
Estimation Based on High, Low, Open, and Close Prices",
The Journal of Business, 73(3), 477-492.
yangZhangSigma(length)
Yang-Zhang volatility estimator. Minimum-variance, unbiased,
drift-independent, and consistent with opening gaps
(Yang & Zhang, 2000). Uses the unbiased sample variance
(biased = false) for both the overnight and open-to-close
components, matching the estimator's unbiasedness claim.
Parameters:
length (simple int) : (simple int) Rolling window length. Must be >= 2.
Returns: (series float) Per-bar sigma, floored at 1e-10.
toX(bars, lookback, mode)
Dimensionless horizontal coordinate.
Parameters:
bars (int) : (series int) Signed bar distance from the anchor.
lookback (int) : (series int) Window length acting as the horizontal unit.
mode (series XScale) : (series XScale) Scaling mode.
Returns: (series float) Signed dimensionless x.
toY(price, sigma, lookback, mode)
Dimensionless vertical coordinate.
Parameters:
price (float) : (series float) Price. Must be > 0.
sigma (float) : (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int) : (series int) Window length (used by isotropic mode only).
mode (series XScale) : (series XScale) Scaling mode.
Returns: (series float) Dimensionless y, or na when inputs are invalid.
moveZScore(dLogPrice, sigma, bars)
Z-score of a log-price move over n bars: dLog / (sigma * sqrt(n)).
In isotropic mode this equals tan(theta) of the same move.
Parameters:
dLogPrice (float) : (series float) ln(target) - ln(anchor).
sigma (float) : (series float) Per-bar Yang-Zhang sigma. Must be > 1e-10.
bars (int) : (series int) Number of bars in the move. Must be > 0.
Returns: (series float) The z-score, or na when inputs are invalid.
triangle(td, anchorPrice, anchorBar, targetPrice, targetBar, sig, lookback, mode)
Right triangle between an anchor and a target, computed entirely
in ICS space. Writes results in place into `td` and returns it.
On invalid inputs every field is set to na, so world X never
receives contaminated numbers.
Parameters:
td (TriangleData) : (TriangleData) Output object, updated in place.
anchorPrice (float) : (series float) Anchor price (world A). Must be > 0.
anchorBar (int) : (series int) Anchor bar_index.
targetPrice (float) : (series float) Target price (world A). Must be > 0.
targetBar (int) : (series int) Target bar_index. Must differ from anchorBar.
sig (float) : (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int) : (series int) Horizontal unit window.
mode (series XScale) : (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
pinTriangle(td, anchorPrice, anchorBar, extremePrice, bodyPrice, curBar, sig, lookback, mode)
Pin (wick) triangle with three vertices in ICS space:
A = anchor, B = candle extreme, C = candle body edge.
Side BC is the wick. theta = signed angle at A between AB and AC.
Since xB = xC, the shoelace area reduces exactly to
0.5 * |yB - yC| * |dx|.
Parameters:
td (TriangleData) : (TriangleData) Output object, updated in place.
anchorPrice (float) : (series float) Anchor price (hh or ll). Must be > 0.
anchorBar (int) : (series int) Anchor bar_index.
extremePrice (float) : (series float) Candle extreme (high or low). Must be > 0.
bodyPrice (float) : (series float) Candle body edge. Must be > 0.
curBar (int) : (series int) Current bar_index. Must differ from anchorBar.
sig (float) : (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int) : (series int) Horizontal unit window.
mode (series XScale) : (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
zeroTri(td)
Resets a TriangleData to na. Use when the structure is inactive,
so inactive periods never enter moving averages or normalization
as fake zero values.
Parameters:
td (TriangleData) : (TriangleData) Object to reset, updated in place.
Returns: (TriangleData) The same `td`, for chaining.
TriangleData
One triangle's measurements in ICS space. All fields dimensionless.
Fields:
theta (series float) : Signed hypotenuse angle in degrees; in isotropic mode tan(theta) is the z-score of the move.
dy (series float) : Signed Euclidean magnitude of the hypotenuse.
area (series float) : Triangle area (>= 0).
centroidY (series float) : Vertical centroid of the triangle.
FrozenAnchors
Anchors frozen at a reference bar, plus activity state.
Fields:
hh (series float) : Highest high at the freeze bar (world-A price units).
ll (series float) : Lowest low at the freeze bar (world-A price units).
mid (series float) : Geometric mean sqrt(hh * ll) at the freeze bar.
bar_x (series int) : bar_index of the freeze bar.
time_x (series int) : time of the freeze bar.
is_active (series bool) : Whether the frozen structure is currently active. Library
Gann Time Price Geometry Ver 1.0Gann Time Price Geometry — Ver 1.0
This indicator builds a dynamic Gann Square grid directly on your chart, anchored to automatically detected swing highs and lows. It combines classical Gann geometry with a scoring-based signal engine to highlight high-confluence buy and sell opportunities.
How it works
The script uses a Vector Circle Search to find the best pivot pair within a harmonic window around your chosen Gann number (88 bars by default). It scores each candidate swing by how closely its price-per-bar ratio and duration match the ideal Gann proportion, then anchors the full grid to the winning pair.
What you get on the chart
What is Drawn on the Chart
🔲 Full Square
The outer Gann Square spans your chosen Gann number in bars horizontally, and 2× the detected swing range vertically. This is the master structure everything else is built inside.
🔲 Sub-Squares (4 Inner Cells)
The full square is divided into 4 equal inner cells — 2 columns × 2 rows. Each cell gets its own set of angle lines projected from its corners. This creates nested geometry that gives you finer entry and exit precision within the larger structure.
📐 Angle Lines
1x1 — the true balance angle between price and time, projected from all four corners of both the full square and each sub-cell
2x1 / 1x2 — steeper and shallower angles showing acceleration and deceleration zones
All angles are clamped within their respective square boundaries so the chart stays clean
⏱️ Time Cycle Verticals
Vertical lines mark Gann's 1/8 harmonic divisions of time across the square:
1/2 cycle (orange, prominent) — the most powerful time node, midpoint of the square
1/4 and 3/4 cycles (dashed) — secondary time divisions where reactions are common
1/8 minor cycles (optional) — finer subdivisions for short-term timing
When price reaches an angle line and a time cycle vertical at the same bar — that is a Gann confluence point, and where this indicator focuses its signals.
Signal scoring (max ~10 pts per signal)
Set Min Confluence Score to 3–4 for quality signals. Lower it to 0 to see all geometrically valid touches.
Settings to tune first
Match Gann Number to your timeframe (88 for most, 44 for fast charts)
Check the Info Table — if Swing pts/bar doesn't match Diagonal, update the Swing Diagonal Is dropdown
Adjust Period Divisor to the harmonic you are trading (1/2 suits swing traders)
Alerts included — Gann Buy and Gann Sell, fire on bar close.
First-Time Setup — 3 Steps
Step 1 — Choose your Gann Number
Start with 88 on Daily or 4H charts. Use 44 on 1H or faster. This defines the width of your square in bars.
Step 2 — Match the Diagonal
Open the chart, look at the Info Table. Find Swing pts/bar and the suggest note next to it. If it says "use 2x1", set the Swing Diagonal Is dropdown to 2x1. Green ✅ means you are calibrated correctly.
Step 3 — Set your Confluence Level
Start at 3. If you are getting too many signals, raise it to 4 or 5. If you want to study all geometric touches without filtering, set it to 0.
Works on: Any instrument — stocks, crypto, forex, indices, commodities
Works on: Any timeframe — tune Gann Number to match
Alerts: Gann Buy and Gann Sell included, fire on bar close
Note on Line Limits
PulseWire Pine Script has a 500-line limit. Keep Squares Forward and Squares Backward at 2 or below to stay within this limit. The indicator will silently drop lines if the limit is exceeded.
Indicator
MACD Matrix: Angle & SettlementThis indicator is a comprehensive Multi-Timeframe (MTF) Dashboard designed for technical traders who rely on MACD not just for crossovers, but for Momentum Angle and Settlement (Hooks).
Instead of cluttering your screen with 5 different MACD charts, this Matrix calculates the math in the background and presents a clean "Heads-Up Display" of the MACD state across your specific timeframes (Default: 3m, 15m, 1h, 4h, 16h).
The Concept: "Angle Settlement"
Standard MACD indicators only show you when a cross happens. By then, the move is often halfway over. This script focuses on the Angle (Slope) of the MACD line to predict turns before they happen:
Steep Angle: Momentum is accelerating. (Strong Trend)
Settling Angle: The slope is flattening out. The MACD line is "hooking." (Reversal/Cross Imminent)
Dashboard Columns Explained
TF (Timeframe): Auto-formats your settings into readable text (e.g., "240" becomes "4h").
Zone:
> 0 (Green): MACD is above the Zero Line (Bullish Trend context).
< 0 (Red): MACD is below the Zero Line (Bearish Trend context).
Cross:
PCO (Green): Positive Crossover (MACD > Signal).
NCO (Red): Negative Crossover (MACD < Signal).
Deg (°):
The calculated mathematical angle of the MACD line.
Positive (+): Momentum is rising.
Negative (-): Momentum is falling.
State (The Strategy):
STEEP (Bright Color): The angle is increasing. Do not trade against this momentum.
SETTLE (Dim Color): The angle is decreasing compared to the previous bar. The momentum is "cooling off," often signaling a "Hook" or an upcoming crossover.
Settings & Customization
Custom Timeframes: You can freely change TF-1, TF-2, etc., in the settings. The table labels will auto-update (e.g., if you change 4h to 1D, the table will display "1D").
MACD Lengths: Fully customizable (Default 12, 26, 9).
Angle Sensitivity: A multiplier to calibrate the "Degrees" to your specific asset class (Crypto, Forex, or Indices). If angles look too small, increase this value. Indicator
Indicator
Indicator
Indicator
Moving Averages With Continuous Periods [macp]This script reimagines traditional moving averages by introducing floating-point period calculations, allowing for fractional lengths rather than being constrained to whole numbers. At its core, it provides SMA, WMA, and HMA variants that can work with any decimal length, which proves especially valuable when creating dynamic indicators or fine-tuning existing strategies.
The most significant improvement lies in the Hull Moving Average implementation. By properly handling floating-point mathematics throughout the calculation chain, this version reduces the overshoot tendencies that often plague integer-based HMAs. The result is a more responsive yet controlled indicator that better captures price action without excessive whipsaw.
The visual aspect incorporates a trend gradient system that can adapt to different trading styles. Rather than using fixed coloring, it offers several modes ranging from simple solid colors to more nuanced three-tone gradients that help identify trend transitions. These gradients are normalized against ATR to provide context-aware visual feedback about trend strength.
From a practical standpoint, the floating-point approach eliminates the subtle discontinuities that occur when integer-based moving averages switch periods. This makes the indicator particularly useful in systems where the MA period itself is calculated from market conditions, as it can smoothly transition between different lengths without artificial jumps.
At the heart of this implementation lies the concept of continuous weights rather than discrete summation. Traditional moving averages treat each period as a distinct unit with integer indexing. However, when we move to floating-point periods, we need to consider how fractional periods should behave. This leads us to some interesting mathematical considerations.
Consider the Weighted Moving Average kernel. The weight function is fundamentally a slope: -x + length where x represents the position in the averaging window. The normalization constant is calculated by integrating (in our discrete case, summing) this slope across the window. What makes this implementation special is how it handles the fractional component - when the length isn't a whole number, the final period gets weighted proportionally to its fractional part.
For the Hull Moving Average, the mathematics become particularly intriguing. The standard HMA formula HMA = WMA(2*WMA(price, n/2) - WMA(price, n), sqrt(n)) is preserved, but now each WMA calculation operates in continuous space. This creates a smoother cascade of weights that better preserves the original intent of the Hull design - to reduce lag while maintaining smoothness.
The Simple Moving Average's treatment of fractional periods is perhaps the most elegant. For a length like 9.7, it weights the first 9 periods fully and the 10th period at 0.7 of its value. This creates a natural transition between integer periods that traditional implementations miss entirely.
The Gradient Mathematics
The trend gradient system employs normalized angular calculations to determine color transitions. By taking the arctangent of price changes normalized by ATR, we create a bounded space between 0 and 1 that represents trend intensity. The formula (arctan(Δprice/ATR) + 90°)/180° maps trend angles to this normalized space, allowing for smooth color transitions that respect market volatility context.
This mathematical framework creates a more theoretically sound foundation for moving averages, one that better reflects the continuous nature of price movement in financial markets. The implementation recognizes that time in markets isn't truly discrete - our sampling might be, but the underlying process we're trying to measure is continuous. By allowing for fractional periods, we're creating a better approximation of this continuous reality.
This floating-point moving average implementation offers tangible benefits for traders and analysts who need precise control over their indicators. The ability to fine-tune periods and create smooth transitions makes it particularly valuable for automated systems where moving average lengths are dynamically calculated from market conditions. The Hull Moving Average calculation now accurately reflects its mathematical formula while maintaining responsiveness, making it a practical choice for both systematic and discretionary trading approaches. Whether you're building dynamic indicators, optimizing existing strategies, or simply want more precise control over your moving averages, this implementation provides the mathematical foundation to do so effectively. Indicator
Quick scan for drift🙏🏻
ML based algorading is all about detecting any kind of non-randomness & exploiting it, kinda speculative stuff, not my way, but still...
Drift is one of the patterns that can be exploited, because pure random walks & noise aint got no drift.
This is an efficient method to quickly scan tons of timeseries on the go & detect the ones with drift by simply checking wherther drift < -0.5 or drift > 0.5. The code can be further optimized both in general and for specific needs, but I left it like dat for clarity so you can understand how it works in a minute not in an hour
^^ proving 0.5 and -0.5 are natural limits with no need to optimize anything, we simply put the metric on random noise and see it sits in between -0.5 and 0.5
You can simply take this one and never check anything again if you require numerous live scans on the go. The metric is purely geometrical, no connection to stats, TSA, DSA or whatever. I've tested numerous formulas involving other scaling techniques, drift estimates etc (even made a recursive algo that had a great potential to be written about in a paper, but not this time I gues lol), this one has the highest info gain aka info content.
The timeseries filtered by this lil metric can be further analyzed & modelled with more sophisticated tools.
Live Long and Prosper
P.S.: there's no such thing as polynomial trend/drift, it's alwasy linear, these curves you see are just really long cycles
P.S.: does cheer still work on TV? @admin Indicator
Trend AngleThe "Trend Angle" indicator serves as a tool for traders to decipher market trends through a methodical lens. It quantifies the inclination of price movements within a specified timeframe, making it easy to understand current trend dynamics.
Conceptual Foundation:
Angle Measurement: The essence of the "Trend Angle" indicator is its ability to compute the angle between the price trajectory over a defined period and the horizontal axis. This is achieved through the calculation of the arctangent of the percentage price change, offering a straightforward measure of market directionality.
Smoothing Mechanisms: The indicator incorporates options for "Moving Average" and "Linear Regression" as smoothing mechanisms. This adaptability allows for refined trend analysis, catering to diverse market conditions and individual preferences.
Functional Versatility:
Source Adaptability: The indicator affords the flexibility to select the desired price source, enabling users to tailor the angle calculation to their analytical framework and other indicators.
Detrending Capability: With the detrending feature, the indicator allows for the subtraction of the smoothing line from the calculated angle, highlighting deviations from the main trend. This is particularly useful for identifying potential trend reversals or significant market shifts.
Customizable Period: The 'Length' parameter empowers traders to define the observation window for both the trend angle calculation and its smoothing, accommodating various trading horizons.
Visual Intuition: The optional colorization enhances interpretability, with the indicator's color shifting based on its relation to the smoothing line, thereby providing an immediate visual cue regarding the trend's direction.
Interpretative Results:
Market Flatness: An angle proximate to 0 suggests a flat market condition, indicating a lack of significant directional movement. This insight can be pivotal for traders in assessing market stagnation.
Trending Market: Conversely, a relatively high angle denotes a trending market, signifying strong directional momentum. This distinction is crucial for traders aiming to capitalize on trend-driven opportunities.
Analytical Nuance vs. Simplicity:
While the "Trend Angle" indicator is underpinned by mathematical principles, its utility lies in its simplicity and interpretative clarity. However, it is imperative to acknowledge that this tool should be employed as part of a comprehensive trading strategy , complemented by other analytical instruments for a holistic market analysis.
In essence, the "Trend Angle" indicator exemplifies the harmonization of simplicity and analytical rigor. Its design respects the complexity of market behaviors while offering straightforward, actionable insights, making it a valuable component in the arsenal of both seasoned and novice traders alike. Indicator
Indicator
Indicator
Indicator
Indicator
TrigLibrary "Trig"
Trigonometric functions
rt_get_angleAlpha(a, b, c, deg)
Get angle α of a right triangle, given the lengths of its sides
Parameters:
a : length of leg a (float)
b : length of leg b (float)
c : length of hypotenuse (float)
deg : flag to return angle in degrees (bool - default = false)
Returns: angle α in radians (or degrees if deg == true)
rt_get_angleAlphaFromLine(x1, y1, x2, y2, l, deg)
Get angle α of a right triangle formed by the given line
Parameters:
x1 : x coordinate 1 (int - optional, required if argument l is not specified)
y1 : y coordinate 1 (float - optional, required if argument l is not specified)
x2 : x coordinate 2 (int - optional, required if argument l is not specified)
y2 : y coordinate 2 (float - optional, required if argument l is not specified)
l : line object (line - optional, required if x1, y1, x2, and y2 agruments are not specified)
deg : flag to return angle in degrees (bool - default = false)
Returns: angle α in radians (or degrees if deg == true)
rt_get_angleBeta(a, b, c, deg)
Get angle β of a right triangle, given the lengths of its sides
Parameters:
a : length of leg a (float)
b : length of leg b (float)
c : length of hypotenuse (float)
deg : flag to return angle in degrees (bool - default = false)
Returns: angle β in radians (or degrees if deg == true)
rt_get_angleBetaFromLine(x1, y1, x2, y2, l, deg)
Get angle β of a right triangle formed by the given line
Parameters:
x1 : x coordinate 1 (int - optional, required if argument l is not specified)
y1 : y coordinate 1 (float - optional, required if argument l is not specified)
x2 : x coordinate 2 (int - optional, required if argument l is not specified)
y2 : y coordinate 2 (float - optional, required if argument l is not specified)
l : line object (line - optional, required if x1, y1, x2, and y2 agruments are not specified)
deg : flag to return angle in degrees (bool - default = false)
Returns: angle β in radians (or degrees if deg == true) Library
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Radar Screen v3This is a combination of various indicators that very rarely conflict, thus giving us a good understanding:
- "Price Rally" detecting whether price is rallying, giving us confidence it will continue.
- Volume - knowing volume is going with the trend is a good confidence check.
- Trend Angle - This will go red or green depending on whether the price angle is going up or down, taken over three bars.
- VWAP for all of these stock traders.
- EMA8 is a very sensitive moving average, good for short term trades.
- CCI SMA is a strategy I commonly use, please check out my other indicators for a functional description.
- Stochastics is used throughout many systems.
- RSI BB shows where price is rebounding of the bollinger band and then moving up or down.
As per all of my indicators, the system is simple - The more green lines you see, the stronger the buy signal. The more red lines you see, the stronger the sell. If its a 50/50 mix of red and green, then don't trade.
I can customise this further or add other strategies, please message me.
Indicator
Indicator
Indicator
