The main part of a mushroom is not the visible fruiting body but they mycelium below the ground – showing the typical fractal branching patterns.
But also the gills of many mushrooms show fractal branching, like f.e. the oyster mushroom, photo below.
The mycelium is forming a symbiosis with the root networks of plants, exchanging water and nutrients the plant wouldn’t reach otherwise for carbohydrates like glucose the mushroom can’t produce on it’s own.
Also, the mycelium can grow much finer networks than plant roots, thus increasing the reach of the plants root system many times over.