|noise(p)| + ½ |noise(2p)| + ¼ |noise(4p)| ...

The application of the absolute value causes a bounce or crease in the noise function in all the places where its value crosses zero. When these modified noise functions are then summed over many scales, the result is visual cusps - discontinuities in gradient - at all scales and in all directions. The visual appearance is consistent with a licking flame-like effect, if it's colored properly. In 1984 I started calling this formulation turbulence, since it gives an appearance of turbulent flow.