Self-similarity is why we instinctively like this image.

The quality of being ‘self-similar’ or ‘fractal’ means the whole has the same shape as one or more of the parts.

A fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, looks very similar to the whole image. Some quick visual examples:(en.wikipedia.org/wiki/F…)

Fractals, described by non-linear equations, emerged in 20th-century complexity science. Scientists soon realised nature was full of them—from ferns and broccoli to coastlines, rivers and snowflakes.

By relying on a non-linear equation you can replicate these natural formations far more effectively than through Euclidean geometry.

The reason why we find ‘self-similarity’ beautiful is still linked to traditional aesthetics - the 3 qualities of beauty outlined by Aquinas: wholeness, harmony of parts and intelligibility. Fractals do seem to call the quality of ‘wholeness’ into question, since you can zoom in or out infinitely and still never see them in their entirety; yet it’s interesting to note that in nature there are only partial fractals - self similarity never repeats itself infinitely.

Photo: Avignon, Palace of the popes. In this case, the ‘generative rule’ of the fractal is given by the pointed arch - larger arches being composed of smaller ones.