Subject: How are symmetrical physical traits stored in DNA?

First let me ask about bilateral symmetry, which  seems so pervasive in the 
animal kingdom, at least in terms of form.  What I want to know is whether 
symmetrical information is stored in a separate gene for each side of an 
organism, or in a single gene, so that a single mutation could account for 
the same (evolutionary) change in both the left and right side.  I ask 
because I was wondering if the way traits are stored allows for easy 
"symmetrical" evolution.

Also, for radial symmetry, could a single mutation account for an identical 
change in, say, each arm of a starfish?

And what about the fractal symmetry that some plants seem to exhibit?

Thanks!

Re: How are symmetrical physical traits stored in DNA?