Metallic Retracement Levels

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There's something that's always bothered me about how traders use Fibonacci retracements. Everyone treats the golden ratio like it's the only game in town, but mathematically speaking, it's completely arbitrary. The golden ratio is just the first member of an infinite family of metallic means, and there's no particular reason why 1.618 should be special for markets when we have the silver ratio at 2.414, the bronze ratio at 3.303, and literally every other metallic mean extending to infinity. We just picked one and decided it was magical.

The metallic means are a sequence of mathematical constants that generalize the golden ratio. They're defined by the equation x² = kx + 1, where k is any positive integer. When k equals 1, you get the golden ratio. When k equals 2, you get the silver ratio. When k equals 3, you get bronze, and so on forever. Each metallic mean generates its own set of ratios through successive powers, just like how the golden ratio gives you 0.618, 0.382, 0.236 and so forth. The silver ratio produces a completely different set of retracement levels, as does bronze, as does any arbitrary metallic number you want to choose.

This indicator calculates these metallic means using the standard alpha and beta formulas. For any metallic number k, alpha equals (k + sqrt(k² + 4)) / 2, and we generate retracement ratios by raising alpha to various negative powers. The script algorithmically generates these levels instead of hardcoding them, which is how it should have been done from the start. It's genuinely silly that most fib tools just hardcode the ratios when the math to generate them is straightforward. Even worse, traditional fib retracements use 0.5 as a level, which isn't even a fibonacci ratio. It's just thrown in there because it seems like it should be important.

The indicator works by first detecting swing points using the Sylvain Zig-Zag. The zig-zag identifies significant price swings by combining percentage change with ATR adjustments, filtering out noise and connecting major pivot points. This is what drives the retracement levels. Once a new swing is confirmed, the script calculates the range between the last two pivot points and generates metallic retracement levels from the most recent swing low or high.

You can adjust which metallic number to use (golden, silver, bronze, or any positive integer), control how many power ratios to display above and below the 1.0 level, and set how many complete retracement cycles you want drawn. The levels extend from the swing point and show you where price might react based on whichever metallic mean you've selected. The zig-zag settings let you tune the sensitivity of swing detection through ATR period, ATR multiplier, percentage reversal, and additional absolute or tick-based reversal values.

What this really demonstrates is that retracement analysis is more flexible than most traders realize. There's no mathematical law that says markets must respect the golden ratio over any other metallic mean. They're all valid mathematical constructs with the same kind of recursive properties. By making this tool, I wanted to highlight that using fibonacci retracements involves an arbitrary choice, and maybe that choice should be more deliberate or at least tested against alternatives. You can experiment with different metallic numbers and see which ones seem to work better for your particular market or timeframe, or just use this to understand that the standard fib levels everyone uses aren't as fundamental as they appear.

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Sürüm Notları

Fixed max line/label issue.
Fixed bar_index issue with lines.
Fixed issue with min ratio

13 saat önce

Sürüm Notları

1. Added center line
   
2. Fixed min level glitch
   
3. Simplified background
   

1 saat önce

Sürüm Notları

Major Update: Dual Zigzag Implementation & Fractional Metallic Numbers

This update adds the TradingView pivot-based zigzag algorithm as an alternative to the original Sylvain implementation. The TradingView method uses pivot point detection with configurable depth rather than real-time percentage reversals, which gives you a different way to identify swings. It looks back a specific number of bars to confirm pivot highs and lows, then checks if the price deviation from the last pivot exceeds an ATR-based threshold. This approach is more retrospective and tends to produce cleaner, less reactive zigzag lines compared to Sylvain's forward-looking method.

You can now switch between the two zigzag styles in the settings. The Sylvain style remains the default and uses percentage reversal combined with ATR, absolute, and tick-based adjustments. The TradingView style uses depth and deviation threshold parameters. Both styles share the same ATR period setting, but they apply it differently. The choice between them depends on whether you want more immediate swing detection or more confirmed, stable pivots.

The script also now supports fractional metallic numbers, not just integers. You can use values like 1.5 or 2.25 instead of being limited to 1, 2, 3, etc. This opens up a much wider range of ratio sequences to experiment with. The metallic mean formula x² = kx + 1 works perfectly fine with non-integer values of k, so there's no mathematical reason to restrict it to whole numbers. This was always possible but just required enabling it in the input configuration.

There's also an "Instant Update" toggle that changes when retracement levels redraw. When enabled, the levels update in real-time as the current swing develops, using the most recent pivot as the endpoint. When disabled, levels only draw once a swing is fully confirmed with a direction reversal. The instant mode gives you forward-looking levels, while the confirmed mode only shows historical levels. Both approaches are valid depending on whether you're trying to anticipate moves or only mark confirmed structure.

The core mathematics and level generation remain identical. The update just gives you more control over how swings are detected and when levels are drawn. The original description covers the metallic mean calculations and why this approach is more flexible than hardcoded fib ratios, and that hasn't changed. This is purely about expanding the zigzag detection options and removing arbitrary restrictions on metallic number values.