The key term F ( ∂ ∂ h ( x , t ) ∂ ∂ x ) , the deterministic part of the growth, is assumed to be a function only of the slope, and to be a symmetric function. A great observation of Kardar, Parisi, and Zhang (KPZ) was that while a surface grows in a normal direction (to the surface), we are measuring the height on the height axis, which is perpendicular to the space axis, and hence there should appear a nonlinearity coming from this simple geometric effect. When the surface slope ∂ ∂ x h = ∂ ∂ h ∂ ∂ x is small, the effect takes the form F ( ∂ ∂ x h ) = ( 1 + | ∂ ∂ x h | 2 ) − − 1 2 , but this leads to a seemingly intractable equation. To circumvent this difficulty, one can take a general F and expand it as a Taylor series,