Basically, we say this because the process of snowflake formation is so complex. Snowflakes form differently based on a variety of factors — temperature, air currents, humidity, and even the presence of impurities in the water such as dirt. Snowflakes also encounter variations in temperature and environmental conditions, melting and reforming many times as it falls.
The short answer to the question is yes, it is indeed extremely unlikely that two complex snowflakes will look exactly alike. It’s so extremely unlikely, in fact, that even if you looked at every one ever made you would not find any exact duplicates.
The long answer is a bit more involved, it depends on just what you mean by “alike,” and on just what you mean by “snowflake.”
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