Lovecraft and Fractal Geometry: Infinite patterns in strange worlds

 

A mandlebulb fractal, Brendan Sapp

 

Introduction: When literature meets mathematics

Sometimes ideas from very different corners of human thought seem to meet in the middle. H.P. Lovecraft, who wrote his unsettling tales of cosmic horror in the early 20th century, never lived to see the usage of the term fractal geometry, a branch of mathematics that really began to develop in the 1970s through the work of Benoît Mandelbrot. And yet, when you place Lovecraft’s descriptions of alien cities and impossible landscapes next to the shapes we now call fractals, the connection feels immediate.

Why does it work so well? Is it just coincidence, or is there something in the way our minds respond to patterns that makes both Lovecraft’s writing and fractal geometry point toward the same sense of mystery? Let’s walk through these strange similarities.

What is Fractal Geometry?

Fractal geometry studies shapes and patterns that repeat endlessly, no matter how closely you look. A good example is a coastline: from far away, it’s jagged. Zoom in on a small section, and it still looks jagged in almost the same way. That repeating, self-similar quality is at the heart of fractals.

Unlike classical geometry, which deals with circles, triangles, and squares, fractals often appear irregular, rough, or infinitely detailed. The famous Mandelbrot set is a perfect example: generated from a simple formula, yet filled with spirals, tendrils, and smaller copies of itself that go on forever.

When you think about it, doesn’t that endless repetition feel like something out of Lovecraft’s imagination—structures or beings that stretch into infinity, beyond our ability to comprehend them?

 Howard Philips Lovecraft, June 1934

Lovecraft’s Non-Euclidean Geometry

Anyone who has read Lovecraft will remember his fascination with what he called non-Euclidean geometry. In The Call of Cthulhu, sailors stumble upon a city where angles behave in ways that simply don’t exist in the human world. In At the Mountains of Madness, explorers in Antarctica find ancient ruins with proportions so vast and so strange that their senses falter.

Lovecraft wasn’t using “non-Euclidean” in a strict mathematical way. For him, it was a description for geometry so alien and unnatural that it couldn’t be fitting within normal human experience, which was fitting within his fascinating worlds. Yet this idea, of spaces that twist and repeat in ways that don’t fit our intuition, sits very close to the feeling that fractal geometry can give.

Overlaps between Lovecraft and Fractal Geometry

So how exactly do these two worlds—Lovecraft’s horror and fractal geometry—speak to each other? A few clear overlaps stand out:

1. Infinity

Lovecraft’s monsters and settings are endless in scale: whether it’s the vast void of space or the immeasurable and indescribable bodies of the Old Ones.

Fractals reveal infinite detail. You can zoom forever and never reach the end.

2. Alien Shapes

Lovecraft’s beings are often described as impossible to fit into human categories, with tentacles, ridges, and branching forms that break anatomy.

Fractal images naturally produce branching trees, curling shells, and shapes that look alive yet unnatural.

3. The Sublime

Lovecraft’s stories are built on the terror of the unknown—the shock of facing something too big for the human mind's comprehension.

Fractals strike a similar chord: simple equations that give rise to patterns so intricate they feel overwhelming.

Lovecraft's literary passages that feel “Fractal”

It’s one thing to talk in theory, but let’s look at a few examples in Lovecraft’s stories that sound almost fractal-like in hindsight:

R’lyeh in The Call of Cthulhu: The city of Cthulhu rises from the sea with alien proportions, endless in its scale, with angles that repeat and twist. Many readers imagine it as something close to a fractal city—spirals within spirals, towers that echo each other at different scales.

The ruins in At the Mountains of Madness: The Antarctic city of the Old Ones is built with layers of repeating structures, from murals to tunnels to halls within halls. It feels recursive, as if exploring it means falling deeper into the same structure over and over.

The growth in The Colour Out of Space: The alien “colour” spreads through the land in creeping, branching forms. Its spread resembles fractal diffusion—an organic growth that repeats itself in unpredictable but familiar ways.

 3D fractal render, Caden Torney

Why does this connection resonates with us

Of course, Lovecraft never knew about the concrete term of fractal geometry. But the reason the connection feels so strong is that both touch on the same emotional and visual space: the awe of infinity.

Lovecraft built that sense of awe through fiction, by describing spaces and beings that bend and defy the rules of reality. Fractal geometry arrives at the same feeling through mathematics, where a simple rule generates infinite complexity. Both lead us to the edge of comprehension, and beyond, where wonder and fear mix.

Fractal Geometry as a lens for Lovecraft

In our time, artists often show fractal alien landscapes, and more often than not, viewers describe them as “Lovecraftian.” Why? Because the spirals, jagged towers, and organic shapes resemble the very cities and creatures Lovecraft hinted at.

You could even argue that fractal geometry gives us a visual key to something Lovecraft could only suggest with words. His descriptions of non-Euclidean geometry now have a modern mathematical counterpart. Looking at a fractal feels like stepping into one of his stories: the same strange beauty, the same sense of dread.

Conclusion: lnfinity in two languages

So, is there a direct historical tie between Lovecraft and fractal geometry? Not the direct one, in the sense that he knew about the term and used it. But he knew about non-Euclidean geometry. The themes of his writings and the looks of fractal geometry echo each other. Both point to an infinity that overwhelms the human mind, going against simple and anthropocentric systems, whether told through equations or through eerie tales of the Old Ones.

Perhaps that’s why fractal geometry feels so at home in the world of Lovecraft. His "monsters", his cities, his landscapes—many could be seen as visual metaphors for the complex themes of his and our time and similar to patterns we now explore with fractals.

What about you, dear reader? When you look at fractal images, do you feel a hint of Lovecraft’s worlds creeping in? Or do you see them as purely mathematical, without the cosmic dread? I guess the answer depends on your interest in Lovecraft and preferences in literature. Share your thoughts below—I’d love to hear how others connect these two.