As Nassim Nicholas Taleb learned from Benoît Mandelbrot, nature is "rough, fractal, and unpredictable." In his groundbreaking book The Black Swan, Taleb showed us how rare, high-impact events dominate our world, from financial crashes to historical turning points. Now, we're discovering that the same fractal patterns that govern stock market crashes also control how metals corrode and fail.

What is Pitting Corrosion? The hidden infrastructure threat

Imagine a bridge, an oil pipeline, or a chemical plant. These structures rely on stainless steel, a metal protected by an invisible oxide film, like a microscopic suit of armour. But in the presence of salt water, this armour can suddenly fail through a process called pitting corrosion. Unlike uniform rust that you can see coming, pitting creates tiny, deep holes that can cause catastrophic failure without warning. These concentrated attacks work like invisible drills, boring deep into the metal while leaving the surface seemingly intact (like termites hollowing out a wooden beam from the inside).

Here's the problem: engineers have traditionally treated pitting like weather forecasters treat rain, using bell curves and averages. But what if pitting is more like earthquakes or market crashes, following the wild, fractal patterns Mandelbrot discovered?

Two types of Pitting Corrosion: Sudden collapse vs progressive failure

Our research at the Université libre de Bruxelles/Université de Mons, conducted in collaboration with AI consultancy company IAlto (full research paper available in npj Materials Degradation), revealed something that corrosion experts have long been aware of but never properly distinguished in their data: stable pitting can happen in two distinctly different ways.

Path 1 - The sudden collapse: like the 2008 financial crisis that seemed to come from nowhere, this type of pitting occurs when the metal's protective layer suddenly breaks down, immediately transitioning to aggressive corrosion.

Path 2 - Death by a thousand cuts: like how small bank failures can cascade into a systemic crisis, this path involves multiple small "metastable" pits that appear and disappear, weakening the metal until one finally breaks through to create permanent damage.

While any corrosion scientist could tell you these two pathways exist conceptually, here's the shocking truth: the field has never distinguished between them in data analysis. For decades, we've treated all critical pitting potentials (Epit, also known as pitting potential) the same, regardless of whether the current density suddenly jumped from a quiet passive state or emerged from a battlefield of pre-existing metastable events.

The second path is particularly insidious because it happens at higher current levels and can occur at lower voltages, making it both harder to detect and potentially more dangerous. Yet until now, both pathways were lumped together in our models and standards.

From a data detection perspective, this second pathway is especially problematic because:

1. It emerges from an already active baseline with metastable events, making the transition to stable pitting less obvious in the data;
2. Traditional analysis methods focus on sudden jumps or clear transitions, which Path 2 doesn't exhibit;
3. The signal-to-noise ratio is lower, as metastable events can mask the critical moment when stable pitting begins.

Using Fractal Analysis to detect rare corrosion events

Taleb warns us about the "Great Intellectual Fraud" of assuming bell curves in complex phenomena. Traditional corrosion analysis makes this exact mistake, missing the rare but catastrophic events hidden in the data's fat tails.

To solve this, we turned to Mandelbrot's fractal mathematics and Principal Component Analysis (PCA). Just as Mandelbrot showed that coastlines have infinite detail at every scale, we discovered that corrosion data exhibits similar fractal properties. By transforming our potentiodynamic polarisation measurements into what we call "Mandelbrot space" and then applying PCA, rare pitting events that would be invisible in normal analysis suddenly stand out like lighthouses in fog.

The Striped Swan: A Black Swan in disguise

If stable pitting events are Taleb's Black Swans (rare, high-impact, and hard to predict), then Path 2 represents something even more elusive: what we call the "Striped Swan." While sudden pitting failures (Path 1) are classic Black Swans that appear from nowhere like the 2008 financial crisis, Path 2 events are Black Swans that arrive wearing deceptive camouflage. They don't come as a single dramatic shock, but as multiple smaller metastable events (the "stripes") that mask their true danger until one finally breaks through to create permanent damage.

Traditional analysis methods are designed to spot regular Black Swans: the sudden passivity breakdown. But Striped Swans slip through our detection systems because they don't look catastrophic until it's too late. Each metastable pit is like a stripe on the swan, and only when enough stripes accumulate does the true nature of the threat reveal itself.

The precautionary principle in action

Our fractal-inspired framework achieved 95% accuracy in detecting these Striped Swans: the metastability-driven pitting events that are rarer and potentially more dangerous than regular Black Swans. This matters because in domains with fat-tailed distributions, missing even one rare event can lead to ruin.

The practical implications are profound. Instead of relying on average corrosion rates, engineers can now:

• Identify which metals/alloys are experiencing the more dangerous metastability-driven pathway;
• Set operating conditions that account for rare but catastrophic pitting events;
• Design monitoring systems that watch for the fractal signatures of impending failure.

Corrosion Prevention strategies: Building antifragile systems

Taleb's concept of antifragility (systems that get stronger under stress) points the way forward ... By understanding pitting's fractal nature, we can design materials and protection systems that don't just resist corrosion but actively adapt to it.

This represents a fundamental shift in materials design. Instead of trying to predict exactly when and where pitting will occur (impossible in a fractal system), we accept uncertainty and build resilience into our materials and monitoring strategies. The engineering world already has an arsenal of protective strategies: self-healing coatings that repair damage autonomously, sacrificial coatings that corrode preferentially to protect the underlying metal, corrosion inhibitors that form protective barriers, and cathodic protection systems that use electrical currents to prevent corrosion. But now, armed with fractal insights, we can deploy these tools more intelligently, targeting the specific pathways and risk patterns our analysis reveals.

The bottom line

By embracing Mandelbrot's "roughness and fractality of reality," we move from predicting damage to building materials and systems that can withstand the unpredictable. In a world where a single deep pit can cause disaster, thinking fractally isn't just academic: it's essential for safety.

As Taleb reminds us: "The inability to predict outliers implies the inability to predict the course of history." In corrosion as in finance, the outliers are what matter most when crisis strikes. Now we have the tools to find both the Black Swans and the even rarer Striped Swans before they find us.

About the research: This breakthrough in corrosion science combines fractal mathematics with materials engineering. For technical details, see the full paper “Identifying stable pitting pathways in 316L stainless steel via fractal-inspired PCA-based clustering” in npj Materials Degradation.