Duszekjk Jacek Kałużny

$$G(x, y) = \sum_{i=0}^{n} \left(w_i \cdot \mathrm{grad}(p_i, x, y)\right)$$

$ G(x, y) $ – noise value at point $ (x, y) $
$ w_i $ – weight
$ \mathrm{grad}(p_i, x, y) $ – dot product of the gradient at grid point $ p_i $ toward $ (x, y) $
$ n $ – number of surrounding grid points

$$V(x, y) = \min_{p_i} \left(d(p_i, (x, y))\right)$$

$ V(x, y) $ – noise value at point $ (x, y) $
$ p_i $ – randomly placed points
$ d(p_i, (x, y)) $ – Euclidean distance between $ p_i $ and $ (x, y) $

$$S(x, y) = \mathrm{interp}\left(v_i, w(x - x_i, y - y_i)\right)$$

$ S(x, y) $ – value noise at point $ (x, y) $
$ v_i $ – random value assigned to grid point
$ w $ – interpolation/smoothing function
$ \mathrm{interp}(...) $ – interpolation between values

$$ \begin{aligned} L(x, y) = w_G \cdot G(x, y) + {} \\ \quad w_V \cdot V(x, y) + w_S \cdot S(x, y) \end{aligned} $$

$ L(x, y) $ – combined noise value
$ w_G, w_V, w_S $ – weights for each component
$ G(x, y), V(x, y), S(x, y) $ – respective noise values