[edsheppa]

A snowflake, for instance, is not an example of self-organizing complexity because it is made structurally complex by external forces.

What external forces? And please don't change the meaning of the word force - the accepted definition is perfectly fine.

[Alamo-Girl]

Thanks for your question!

Snow Crystals, Physics of Snow Crystals

Under what conditions do the different snow crystal types form?

   This is a key point for understanding snow crystals.  By growing snow crystals in the laboratory under controlled conditions, one finds that snow crystals grow in different forms depending on the temperature and humidity in which the crystal grows. This behavior is summarized in a "morphology diagram," which gives the crystal shape under different conditions.

   From this diagram, we see that the crystal shape depends mainly on temperature.  The growth changes from plates around -2 C to columns near -5 C, to plates again near -15 C, and to a combination of plates and columns around -30 C.
   Furthermore, we can see that snow crystals tend to form simpler shapes at lower humidities and more complex shapes at higher humidities.  The most extreme shapes -- long needles around -5C and large thin plates around -15C -- form when the humidity is relatively high. 

Why do snow crystals form such complex shapes in the first place?

   Snow crystal shapes depend on a delicate combination of faceting and branching.  These are explained further in Crystal Faceting and Snowflake Branching.

Why do snow crystals grow differently at different temperatures?

    This is still not known, believe it or not.  The different ice facets grow at different rates in different temperatures, and to date we don't really know why the growth rates depend so strongly on temperature.  The growth depends on exactly how water vapor molecules are incorporated into the growing ice crystal, and the physics behind this is quite complex and not well understood.  It is the subject of current research in my lab and elsewhere.