The principle of the subdivision method is to recursively subdivide (split) polygons of a model up to a required level of detail. At the same time, the parts of the split polygons will be perturbed. The initial shape of the model is retained to an extent, depending on the perturbations. Thus, a central point of the fractal subdivision algorithm is perturbation as a function of the subdivision level.

 

Concerning mountains, the higher the level the smaller the perturbation, otherwise the mountains would get higher and higher. In addition, there must be a random number generator to obtain irregularities within the shape - and to achieve a kind of statistical similarity:

 

P_n = p( n ) * rnd();

Where p_n = perturbation at level n, 
P( ) = perturbation function depending on level n, and 
Rnd( ) = random number generator.

 

X-Cursive is a system that uses the principle of the above by recursively subdividing a triangle while perturbing them to generate more forms.