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Snow flakes form as water freezes in 3-dimensional space while being acted upon by energy leaking in from 4th-dimensional space (aka, Brownian Motion). Viewed in 3-dimensions, snowflakes appear to have different designs. Viewed in 4-dimensions, snowflakes all have the same design -- growth rate centered on square-root-of-time (in any one dimension); surface bounded by an ellipse (in any two dimensions); and surface bounded by a log-spiral (in three dimensions). After all, if snowfakes were strictly of different designs you would not know them as snowflakes when you saw them.

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17y ago

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