Well, ice pillars are caused by flat ice crystals dangling in the air, behaving like small mirrors. The trumpet shape can indeed be explained by the wobbling proposed by Wayne. The argument is basically statistical+geometrical.
The direction in which each of the crystals points is a random vector, centered around the downward direction. The integrated effect of all these microscopic mirrors yields a "blurring" mirror. The reflection of a point source becomes smeared out to an extent proportional to the size of the fluctuations, but also to the distance between observer and the ice crystals responsible for the reflection (this is the geometry bit). Now if you're looking high up, you're seeing the reflection of the point source via ice crystals that are farther away, higher up in the atmosphere. The smearing out caused by these ones is therefore wider than for crystals closer by.
One can give a quantitative mathematical argument for this phenomenon, leading to the formula
![Shocked :shock:](./images/smilies/icon_eek.gif)
cos phi = Sqrt(1- Sin(theta)^2/Cos(alpha)^2)/Cos(theta). Here, theta is the elevation angle of the line of sight (0 if looking towards horizon, pi/2 if looking towards zenith), phi is half the angular width of the pillar, and alpha is an angle measuring how much the orientation of the ice crystals varies (0 for not at all).
If you plot the function, you find that phi is 0 when looking towards the horizon (theta=0) and becomes bigger with increasing theta. For an angle theta satisfying Sin(theta)=Cos(alpha), phi is essentially pi/2, which means the width of the trumpet has become infinite and the light becomes smeared out so widely you hardly see it anymore. You can notice this feature in the picture: the trumpet stops at a certain elevation.
If anyone likes the details of the calculation, pls reply...