Snowflakes are often said to be completely unique; every fluffy flurry that has fallen to the ground does not have an identical companion. While that might be a tough one to prove experimentally, there is a high level of variation from one snowflake to the next, due to the sensitive nature of their formation. While it's theoretically possible to have identical twin snowflakes, it is extremely unlikely.
As tiny cold water droplets get carried up into the atmosphere, they meet microscopic particles in the air (such as pollen or dust) and begin to freeze into an ice crystal. Water's unique ability to expand upon freezing and hydrogen bonding between the water molecules determine the crystal’s shape, forming a symmetrical and hexagonal prism.
As more tiny droplets land and freeze on the crystal, the snowflake continues to grow. This additional freezing water occurs more quickly on the edges, forming cavities that will become the gaps and grooves seen in the final snowflake plate. Six arms begin to grow out of the corners, and the size and shape of those is also impacted by the changing weather conditions as the snowflake gets whipped through the air. However, all of the arms will look pretty much the same, because they were all subjected to the same environmental conditions.
The exact shape of the snowflake is a product of temperature, humidity, amount of water, and the size of the pollen or dust particle. Snowflakes that look like thin hexagonal needles occur in colder air while the most intricate shapes and plates occur when it is slightly warmer and slightly more humid. As the air can change depending on location and elevation, the snowflake’s shape can be influenced in many different ways before it finally comes to rest on the ground.
Filmmaker Vyacheslav Ivanov has created an amazing time-lapse film of the formation of snowflakes. The two-minute-long video is called Snowtime and is pretty much mesmerizing.
Hat tip: i09