Weierstrass + Fractal Cycles
Title: Weierstrass Fractal Cycles —
Regime-Aware Oscillator with Divergence, Trend Gate & Trade Plan
Short description
A mathematically grounded fractal oscillator built on the Weierstrass function (a·b regime), with auto-tuned frequency, confirmed zero-crosses, regular/hidden divergence, trend gating, and a full state-machine trade plan with ATR SL/TP and webhook-ready alerts.
📖 Full Description
🧠 What it is
Most oscillators are recombinations of price averages. This one is different — it's built directly from the Weierstrass function, the classic example of a continuous but nowhere-differentiable curve:
W(x) = Σ aⁿ · cos(bⁿ · π · x)
The behavior of that sum is governed almost entirely by the product a·b, which gives this indicator something rare: a mathematically meaningful regime classification.
a·b Regime Meaning
> 1 🔵 FRACTAL Rough, self-similar, chaotic — the Weierstrass property
≈ 1 🟠 CRITICAL Boundary case, transition zone
< 1 ⚪ SMOOTH Low-dimensional, mean-reverting behavior
The oscillator you see plotted is that sum, normalized and optionally smoothed. Its shape changes with regime — not just its level.
⚙️ How it works
1. Auto Timeframe Detection
On low timeframes (≤15m) the script shortens pivot lengths, reduces terms, and boosts scale. On higher TFs it lengthens them. You don't have to re-tune per chart — but you can disable this and go fully manual.
2. Auto-Tune b (optional)
When enabled, every N bars the script searches b ∈ [bMin, bMax] and picks the value that maximizes a variance-ratio "roughness" score. A ★ appears in the info table when a tuned value is active. A performance guard caps tuning to the first perfGuardMax bars so it never slows your chart down.
3. Anchoring
Bar Index — rolling anchor, always fresh
Swing Pivot — re-anchors to the latest pivot, with a phase-continuity correction so the oscillator never jumps
Fixed Start — anchor to a specific timestamp
4. Confirmed Zero-Crosses
Instead of firing on the first bar past zero, the script requires eff_confirm consecutive bars on the new side. This eliminates most whipsaws while staying responsive.
5. Trend Gate
Signals can be filtered by EMA, SMA, or Supertrend direction. Counter-trend alerts can be allowed separately from counter-trend entries.
6. Divergence Detection
Regular and hidden divergence is detected on price pivots vs. oscillator pivots, with a configurable range cap and optional drawn lines.
7. Trade Plan (state machine)
Optional long/short state machine with:
ATR-based SL/TP
Optional divergence requirement for entry
Opposite-signal rejection
Entry/SL/TP lines drawn on the price chart via force_overlay
JSON or plain-text webhook payloads for automation
8. Info Table
Live readout of: regime, a·b, effective b, scale, oscillator value, trend state, Supertrend direction, last divergence, current plan state, open P&L in ATR multiples, and performance-guard status — all with tooltips.
🎨 How to read the panel
Oscillator line — cyan when rising, yellow when falling
Background tint — regime color (blue = fractal, orange = critical, gray = smooth)
▲ / ▼ arrows — confirmed zero-crosses (bright = trend-aligned, dim = counter-trend)
DIV / hDIV labels — regular and hidden divergence
Circles — Supertrend direction mirrored onto the oscillator panel (a compact visual gate)
Info table — top-right by default; fully configurable position, layout, and size
🛠 Suggested starting configurations
Style TF autoTF a b trendType confirm
Scalp 5–15m ✅ 0.5 auto Supertrend 1
Intraday 1H–4H ✅ 0.5 3.0 EMA 34 2
Swing 1D ✅ 0.5 3.0 EMA 50 2
Position 1W ✅ 0.6 2.5 Supertrend 3
Turn on Auto-Tune b if you want the script to adapt b to the instrument's own texture. Turn it off for reproducibility.
🔔 Alerts available
Zero-cross (bull/bear, trend-gated)
Regime change (FRACTAL / CRITICAL / SMOOTH)
Regular divergence (bull/bear)
Hidden divergence (bull/bear)
Trade plan ENTRY and EXIT (with full JSON payload for webhooks)
All alerts fire once_per_bar_close — designed for reliable bot consumption, not intrabar noise.
⚠️ Notes & limitations
This is not a repainting-free guarantee for divergence drawings — divergence is confirmed only after eff_divLook bars (standard pivot behavior).
Auto-tune is disabled after perfGuardMax bars by design, to keep long charts snappy.
The Weierstrass sum is deterministic given (a, b, x) — it is not predictive in itself. It's a texture measure, not a forecast. Use it as a filter and context tool, not a standalone entry system.
The trade plan is a reference implementation — always forward-test and size positions independently.
The maximum useful n_terms in the UI is capped at 12 internally for performance, even though the input allows 50.
🧪 Philosophy
This indicator treats the market as a signal texture problem rather than a prediction problem. The regime tells you what kind of market you're in; the oscillator tells you where in that texture you are; the trend gate tells you whether to trust the signal direction. Everything else — divergence, plan, alerts — is scaffolding around those three questions.
Trade the regime. Respect the trend. Let the noise stay noise.
📌 Credits
Original concept and implementation by © gogaz. Published under Mozilla Public License 2.0. Built on Pine Script® v6.
Feedback, forks, and instrumentation ideas are welcome — especially if you find a cleaner objective for the auto-tune score or a better phase-continuity correction for pivot anchoring.
Not financial advice. Past behavior of a mathematical function is not a guarantee of future behavior of a financial instrument. Use at your own risk.
Regime-Aware Oscillator with Divergence, Trend Gate & Trade Plan
Short description
A mathematically grounded fractal oscillator built on the Weierstrass function (a·b regime), with auto-tuned frequency, confirmed zero-crosses, regular/hidden divergence, trend gating, and a full state-machine trade plan with ATR SL/TP and webhook-ready alerts.
📖 Full Description
🧠 What it is
Most oscillators are recombinations of price averages. This one is different — it's built directly from the Weierstrass function, the classic example of a continuous but nowhere-differentiable curve:
W(x) = Σ aⁿ · cos(bⁿ · π · x)
The behavior of that sum is governed almost entirely by the product a·b, which gives this indicator something rare: a mathematically meaningful regime classification.
a·b Regime Meaning
> 1 🔵 FRACTAL Rough, self-similar, chaotic — the Weierstrass property
≈ 1 🟠 CRITICAL Boundary case, transition zone
< 1 ⚪ SMOOTH Low-dimensional, mean-reverting behavior
The oscillator you see plotted is that sum, normalized and optionally smoothed. Its shape changes with regime — not just its level.
⚙️ How it works
1. Auto Timeframe Detection
On low timeframes (≤15m) the script shortens pivot lengths, reduces terms, and boosts scale. On higher TFs it lengthens them. You don't have to re-tune per chart — but you can disable this and go fully manual.
2. Auto-Tune b (optional)
When enabled, every N bars the script searches b ∈ [bMin, bMax] and picks the value that maximizes a variance-ratio "roughness" score. A ★ appears in the info table when a tuned value is active. A performance guard caps tuning to the first perfGuardMax bars so it never slows your chart down.
3. Anchoring
Bar Index — rolling anchor, always fresh
Swing Pivot — re-anchors to the latest pivot, with a phase-continuity correction so the oscillator never jumps
Fixed Start — anchor to a specific timestamp
4. Confirmed Zero-Crosses
Instead of firing on the first bar past zero, the script requires eff_confirm consecutive bars on the new side. This eliminates most whipsaws while staying responsive.
5. Trend Gate
Signals can be filtered by EMA, SMA, or Supertrend direction. Counter-trend alerts can be allowed separately from counter-trend entries.
6. Divergence Detection
Regular and hidden divergence is detected on price pivots vs. oscillator pivots, with a configurable range cap and optional drawn lines.
7. Trade Plan (state machine)
Optional long/short state machine with:
ATR-based SL/TP
Optional divergence requirement for entry
Opposite-signal rejection
Entry/SL/TP lines drawn on the price chart via force_overlay
JSON or plain-text webhook payloads for automation
8. Info Table
Live readout of: regime, a·b, effective b, scale, oscillator value, trend state, Supertrend direction, last divergence, current plan state, open P&L in ATR multiples, and performance-guard status — all with tooltips.
🎨 How to read the panel
Oscillator line — cyan when rising, yellow when falling
Background tint — regime color (blue = fractal, orange = critical, gray = smooth)
▲ / ▼ arrows — confirmed zero-crosses (bright = trend-aligned, dim = counter-trend)
DIV / hDIV labels — regular and hidden divergence
Circles — Supertrend direction mirrored onto the oscillator panel (a compact visual gate)
Info table — top-right by default; fully configurable position, layout, and size
🛠 Suggested starting configurations
Style TF autoTF a b trendType confirm
Scalp 5–15m ✅ 0.5 auto Supertrend 1
Intraday 1H–4H ✅ 0.5 3.0 EMA 34 2
Swing 1D ✅ 0.5 3.0 EMA 50 2
Position 1W ✅ 0.6 2.5 Supertrend 3
Turn on Auto-Tune b if you want the script to adapt b to the instrument's own texture. Turn it off for reproducibility.
🔔 Alerts available
Zero-cross (bull/bear, trend-gated)
Regime change (FRACTAL / CRITICAL / SMOOTH)
Regular divergence (bull/bear)
Hidden divergence (bull/bear)
Trade plan ENTRY and EXIT (with full JSON payload for webhooks)
All alerts fire once_per_bar_close — designed for reliable bot consumption, not intrabar noise.
⚠️ Notes & limitations
This is not a repainting-free guarantee for divergence drawings — divergence is confirmed only after eff_divLook bars (standard pivot behavior).
Auto-tune is disabled after perfGuardMax bars by design, to keep long charts snappy.
The Weierstrass sum is deterministic given (a, b, x) — it is not predictive in itself. It's a texture measure, not a forecast. Use it as a filter and context tool, not a standalone entry system.
The trade plan is a reference implementation — always forward-test and size positions independently.
The maximum useful n_terms in the UI is capped at 12 internally for performance, even though the input allows 50.
🧪 Philosophy
This indicator treats the market as a signal texture problem rather than a prediction problem. The regime tells you what kind of market you're in; the oscillator tells you where in that texture you are; the trend gate tells you whether to trust the signal direction. Everything else — divergence, plan, alerts — is scaffolding around those three questions.
Trade the regime. Respect the trend. Let the noise stay noise.
📌 Credits
Original concept and implementation by © gogaz. Published under Mozilla Public License 2.0. Built on Pine Script® v6.
Feedback, forks, and instrumentation ideas are welcome — especially if you find a cleaner objective for the auto-tune score or a better phase-continuity correction for pivot anchoring.
Not financial advice. Past behavior of a mathematical function is not a guarantee of future behavior of a financial instrument. Use at your own risk.
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.