The Sierpiński Triangle, Explained
An equilateral triangle, a simple midpoint rule repeated forever, and zero area remaining — how one Polish mathematician's 1915 curiosity became one of the most recognizable fractals in all of mathematics.
Famous Fractals
Famous Fractals is a recurring topic across Fractal. This hub collects every guide and explainer tagged Famous Fractals, newest first — each grounded in real mathematics and real examples, written to be rigorous yet readable.
The Menger Sponge: Zero Volume, Infinite Surface
A cube riddled with holes until nothing remains — yet its surface never stops growing. Inside the paradox that convinced mathematicians to rethink dimension itself.
The Koch Snowflake: Infinite Perimeter, Finite Area
A Swedish nobleman described a curve in 1904 that broke classical geometry. More than a century later, its paradox still illuminates the deepest ideas in fractal mathematics — and powers the antenna inside your smartphone.
The Dragon Curve & Space-Filling Curves (Hilbert, Peano, Cantor)
From a NASA physicist's paper-folding experiment to a curve that almost fills all of 2D space — meet the dragon curve and its kin: the curves that forced mathematicians to rethink what dimension even means.
3D Fractals: Mandelbulb, Mandelbox & Beyond
In 2009, two hobbyists on an internet forum did what professional mathematicians had sought for decades: they extended the Mandelbrot set into three dimensions. Here is the story of the Mandelbulb, the Mandelbox, and the strange geometry of 3D fractal space.
Frequently asked
What is Famous Fractals?
Famous Fractals is a topic our editors cover across the site. This hub gathers the related guides and explainers so you can read the full picture in one place.
How often is the Famous Fractals hub updated?
This hub updates automatically whenever a new article is tagged Famous Fractals, so the most recent coverage always appears first.
Who writes the Famous Fractals guides?
Every guide here is written by the Fractal editorial desk, with the mathematics checked against primary sources and explained for a general reader.