NEW SEQ?

[zak seidov]

Rows of Binary Sequences

We start with any seed sequence
(of any length and structure), e.g.:
{0,1}

and proceed:
{0,1,1}
{0,1,1,1,0,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1}
......................................................

The rule is 
"Put in  the (binary) sum of neighbors between them!":
{0,0}=>{0,0,0},{0,1}=>{0,1,0},
{1,0}=>{0,1,0},{1,1}=>{1,1,0,1}.

My Q's:
1. Is it known?
1a. If yes, please give Ref/Cf.
1b. If not:
2. Is it interesting?
2a. If yes, what can be said about patterns, cycles,
dependence on seeds etc.
2b. If not, please ignore it.
Thanks, Zak

PS. In case of anyone interested, here's (raw but
working Mmca):
s={0,1};s2=s;Print[s2];Do[j=1;Do[si1={s[[i]],s[[i+1]]};in=Which[si1‰ó{0,0},0,si1‰ó{0,1},1,si1‰ó{1,0},1,si1‰ó{1,1},{1,0}];
s2=Insert[s2,in,i+j];j++,{i,1,Length[s]-1}];
s2=Flatten[s2];Print[s2];s=s2,{5}]
{0,1}
{0,1,1}
{0,1,1,1,0,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1}

__________________________________________________
Do You Yahoo!?
Tired of spam?  Yahoo! Mail has the best spam protection around 
http://mail.yahoo.com