The coastline paradox presents a fascinating challenge to our understanding of geography. It reveals a striking truth: there is no consistent way to measure the length of a country's coastline. The ...

While madeleines may have triggered recherche du temps perdu for Proust, my family finds meaning in mandelbrot. The crunchy layer of cinnamon sugar on top of each slice stirs up memories of ...

Though people had long noticed these special patterns by which the natural world organizes itself, the term fractal was coined about 50 years ago by the mathematician Benoit Mandelbrot, author of ...

Even the fractal pattern that bears his name is created from Julia sets: indeed, focus in on any boundary point of the Mandelbröt set, and it’s functionally the same as a Julia set.

This idea of visualisation from Mandelbrot, who would have turned 100 this month, led mathematicians to accept the role of pictures in experimental mathematics. It has also led to a huge amount of ...

This cyclical behavior then creates patterns that can be recognized and used to predict market changes. Mandelbrot, in writing that's often rare for a mathematician, is very clear on this point: ...

No matter how much you zoom in on the Mandelbrot set, novel patterns always arise, without limit. “It’s completely mind-blowing to me, even now, that this very complex structure emerges from such ...

Fractals differ from ordinary patterns. Unlike a pattern on a shirt that can be reproduced by machines, fractals are generated by “seed algorithms” that are recursively applied.