 An easy way to “smooth” the Hong-Page landscapes is to assign random values not to every point on the 2000-point loop but every second point, for example, with intermediate points taking an average between those on each side. Where a random landscape has a “smoothness” factor of 0, this variation will have a randomness factor of 1. A still “smoother” landscape of degree 2 would be one in which slopes are drawn between random values assigned to every third point. Each degree of smoothness increases the average value correlation between a point and its neighbors. Grim et al. consider landscapes of varying “smoothness” along roughly these lines, though with a randomization that avoids the lock-step intervals suggested (Grim et al. 2019).