[darbymcgill]

More strictly, symmetry typically contains less algorithmic information than asymmetry, and therefore can be generated by simpler machinery.

I can see how symmetry could be more easily replicated once achieved. But it seems to me that the achievement of symmetry via random mutation would be significantly more complex.

What am I missing?

[CarolinaGuitarman]

"I can see how symmetry could be more easily replicated once achieved. But it seems to me that the achievement of symmetry via random mutation would be significantly more complex."

Selection.

[tortoise]

But it seems to me that the achievement of symmetry via random mutation would be significantly more complex.

Symmetry itself is not that remarkable no matter how it is generated -- nature is full of it. All that would be required is for a symmetry generating mutation to confer advantages on the host such that the symmetry would be conserved. In some cases, evolution actually breaks natural symmetry (e.g. flatfish eyes) when it has survival advantages.