Fractals in art

Mathematicians did not invent fractals. People have been building them into art for about a thousand years, long before anyone had a name for them.

Perhaps the oldest fractals made on purpose are in Indian temples. The Kandariya Mahadev Temple at Khajuraho, Madhya Pradesh, finished around 1025 CE, is one tall structure made of smaller copies of itself, and those carry even smaller copies.

Stand far away and you see one temple. Come closer and the same outline repeats in its towers. Closer still, and it repeats again. That is self-similarity carved in stone. The builders made it; mathematicians gave the idea a name about 900 years later.

It is not just one temple. Fractal-like patterns appear in temples at Madurai, Hampi, Rameswaram, Varanasi and many other places.

The same idea appears far away too. Fractals are common in traditional African art. The patterns woven into Nigerian Fulani wedding blankets often have a fractal structure: diamonds, with smaller diamonds inside, and smaller ones inside those. The weaver needed no equation, only the rule of repeating a shape inside itself.

In modern art, the Dutch artist M.C. Escher (the same Escher known for tilings) made a print called 'Smaller and Smaller'. It shows one pattern of lizards repeated at smaller and smaller sizes, closing in towards the centre for ever.