Inverse distribution

Inverse Distribution vs. Normal Distribution

Two new randomizer types: the inverse and inverseAbs. Inverse (or Wald) Distributions are biased against average values, tending towards more extremes. See: https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

A standard wald distribution is represented in COG as the inverseAbs setting, which is not likely to be of much use (as it will produce values biased positively or biased negatively, but not cycle between) but as it is impossible to simulate using the other methods, it is available. Using this value on the SegmentAngle attribute for a vein distribution will lead to cyclic veins that travel in corkscrews with the amount of curvature being random.

The inverse option takes the absolute value nature of the classic wald distribution and mirrors it across the y axis, producing a curve that is balanced between positive and negative results, with “no change” (a zero) being the least common result. Using this value on the SegmentAngle attribute for a vein distribution results in veins that travel generally straight with only slight bends for long distances before suddenly veering off in a new direction very sharply. This is due to the gently biased nature of the wald distribution: the actual “median” value is very close to zero (a multiplier of 0.4 to 0.6) with a quick drop to both sides, but with a long tail out to infinity: most changes will be small, but non-zero, with wild extremes happening occasionally.