Even something as tiny as a snowflake is governed by the laws of order

In addition to plants, some animals, like the nautilus, exhibit Fibonacci numbers. For instance, the shell of a nautilus is grown in a “Fibonacci spiral.” 

The spiral occurs because of the shell’s attempt to maintain the same proportional shape as it grows outward. 

In the case of the nautilus, this growth pattern allows it to maintain the same shape throughout its whole life (unlike humans, whose bodies change proportion as they age).

As is often the case, there are exceptions to the rule—so not every nautilus shell makes a Fibonacci spiral. But they all adhere to some type of logarithmic spiral.

And before you start thinking that these cephalopods could have kicked your butt in math class, remember that they’re not consciously aware of how their shells are growing, and are simply benefiting from an evolutionary design that lets the mollusk grow without changing shape.

Even something as tiny as a snowflake is governed by the laws of order, as most snowflakes exhibit six-fold radial symmetry with elaborate, identical patterns on each of its arms.

Understanding why plants and animals opt for symmetry is hard enough to wrap our brains around, but inanimate objects—how on earth did they figure anything out?

Apparently, it all boils down to chemistry; and specifically, how water molecules arrange themselves as they solidify (crystallize).

Water molecules change to a solid state by forming weak hydrogen bonds with each other. 

These bonds align in an ordered arrangement that maximizes attractive forces and reduces repulsive ones, which happens to form the overall hexagonal shape of the snowflake.

But as we’re all aware, no two snowflakes are alike—so how is it that a snowflake is completely symmetrical with itself, while not matching any other snowflake?

Well, as each snowflake makes its descent from the sky it experiences unique atmospheric conditions, like humidity and temperature, which effect how the crystals on the flake “grow.”

All the arms of the flake go through the same conditions and consequently crystallize in the same way – each arm an exact copy of the other. 

No snowflake has the exact same experience coming down and therefore they all look slightly different from one another.

https://listverse.com/2013/04/21/10-beautiful-examples-of-symmetry-in-nature/