bhaskar saikia

Look closely at a fern leaf, the branching of trees, or the snaking veins of a river seen from the sky. Now zoom in. You’ll find the same patterns repeating again and again, like a quiet mantra whispered across scales. This is the world of fractals—a language through which nature writes its poetry.

A fractal is a never-ending pattern. It is self-similar across different scales, meaning that a small part of it looks like the whole. Mathematically, it’s a concept rooted in complexity—irregular shapes that cannot be described by traditional geometry but unfold beautifully through recursive equations.

But beyond numbers and formulas, fractals are a reminder that life thrives in patterns—visible and hidden.

The cauliflower in your kitchen, the spiral of a galaxy, the rhythmic beating of your heart, even the way coastlines curl and break—these are all expressions of fractal geometry. Benoît Mandelbrot, the mathematician who popularized the term, once called fractals “the geometry of roughness,” embracing the chaos and imperfection that traditional math tried to smooth out.

Fractals are not just about repetition—they’re about depth. They show us that the closer we look, the more we see. They teach us that complexity doesn’t have to be complicated. That what may appear chaotic is often holding onto a secret order.

And perhaps, in a more philosophical sense, fractals are a mirror to our inner lives. Our memories, emotions, dreams—they all repeat in spirals, unfolding and folding into one another. The fears we thought we buried re-emerge in new forms. The joy we once felt as children finds its echo in an afternoon breeze or a favorite song. Life is fractal, too.

So next time you’re out in the wild—or even just sitting by your window—notice the repetitions. Notice the self-similarity. Nature, it seems, is always telling us: there’s beauty in the pattern, and meaning in the return.