Self-Similarity
In mathematics, the characteristic of something being exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar, as parts of them show the same statistical properties at many scales.
Origin
The concept predates its name: mathematician Helge von Koch described self-similar curves in 1904, and Paul Lévy extended them in his 1938 paper on curves "consisting of parts similar to the whole." The modern synthesis came from Benoît Mandelbrot, who wrote about statistical self-similarity in his 1967 Science paper "How Long Is the Coast of Britain?" Mandelbrot coined the term fractal in 1975 from Latin frāctus (broken), connecting these mathematical patterns to real-world structures from coastlines to clouds.