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The study, published in December in Journal of Ecology, refutes claims that the self-similarity which is observed within individual trees can be extended to whole forest canopies and landscapes.

If self-similarity extended from the small twigs of a single tree to entire forest ecosystems, it would help ecologists describe complex landscapes in much simpler ways, and potentially directly compare the complexity of very different ecosystems, such as coral reefs and forest canopies.

By contrast, a regular cauliflower often displays self-similarity in at least seven fractal scales, meaning a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in, ultimately, another spiral.

The defining characteristic of a fractal, such as the Mandelbrot set, “is self-similarity,” Dr. Hart said.

Fractal music also displays self-similarity at varying scales, but applied to, say, pitch and tempo.