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Subdivide Fractal

Mode: Edit mode

Panel: Mesh Tools (Editing context, F9)

Hotkey: W » 3 NumPad

Menu: Mesh » Edges » Subdivide Fractal, Specials » Subdivide Multi Fractal

The sample mesh.
Subdivide Fractal, with a factor of 10.

Subdivide Fractal (found in the Mesh » Edges menu, or as the Fractal button in the Mesh Tools panel) works exactly as Subdivide, except that it randomly translates all vertices created by the subdivision. The level of randomness is set in the Rand fac pop-up numeric field shown by the tool before processing (value between 1 and 100 – I don’t know the unit…).

Subdivide Multi Fractal (located in the Specials pop-up menu) is the “fractal” or random version of Subdivide Multi.