No. You can invent variations on the basic rule to create different patterns.
A Java applet that draws a snowflake is described in chapter 74.
Since no two identical snowflakes have been found in Nature, it is clear that there are many possible variations of the basic rule.
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The path to wisdom does, in fact, begin with a single step. Where people go wrong is in ignoring all the thousands of other steps that come after it.
— Terry Pratchett, Hogfather