[R] How do I generate a grid of data in [0,1]?

[esh]

Hello, my objective is to produce a data.frame that represents a grid of data points evenly spaced as closely together as possible on a graph with domain and range both being [0,1].  I tried to get a smaller example working first and I tried the following code:
> sink(file="Rsampledata")
> a<-0
> while(a<1) {data<-data.frame(a,seq(0,1,0.1)); print(data); a<-a+0.1}

My output was: 
   a seq.0..1..0.1.
1  0            0.0
2  0            0.1
3  0            0.2
4  0            0.3
5  0            0.4
6  0            0.5
7  0            0.6
8  0            0.7
9  0            0.8
10 0            0.9
11 0            1.0
     a seq.0..1..0.1.
1  0.1            0.0
2  0.1            0.1
3  0.1            0.2
4  0.1            0.3
5  0.1            0.4
6  0.1            0.5
7  0.1            0.6
8  0.1            0.7
9  0.1            0.8
10 0.1            0.9
11 0.1            1.0
     a seq.0..1..0.1.
1  0.2            0.0
2  0.2            0.1
3  0.2            0.2
4  0.2            0.3
5  0.2            0.4
6  0.2            0.5
7  0.2            0.6
8  0.2            0.7
9  0.2            0.8
10 0.2            0.9
11 0.2            1.0
     a seq.0..1..0.1.
1  0.3            0.0
2  0.3            0.1
3  0.3            0.2
4  0.3            0.3
5  0.3            0.4
6  0.3            0.5
7  0.3            0.6
8  0.3            0.7
9  0.3            0.8
10 0.3            0.9
11 0.3            1.0
     a seq.0..1..0.1.
1  0.4            0.0
2  0.4            0.1
3  0.4            0.2
4  0.4            0.3
5  0.4            0.4
6  0.4            0.5
7  0.4            0.6
8  0.4            0.7
9  0.4            0.8
10 0.4            0.9
11 0.4            1.0
     a seq.0..1..0.1.
1  0.5            0.0
2  0.5            0.1
3  0.5            0.2
4  0.5            0.3
5  0.5            0.4
6  0.5            0.5
7  0.5            0.6
8  0.5            0.7
9  0.5            0.8
10 0.5            0.9
11 0.5            1.0
     a seq.0..1..0.1.
1  0.6            0.0
2  0.6            0.1
3  0.6            0.2
4  0.6            0.3
5  0.6            0.4
6  0.6            0.5
7  0.6            0.6
8  0.6            0.7
9  0.6            0.8
10 0.6            0.9
11 0.6            1.0
     a seq.0..1..0.1.
1  0.7            0.0
2  0.7            0.1
3  0.7            0.2
4  0.7            0.3
5  0.7            0.4
6  0.7            0.5
7  0.7            0.6
8  0.7            0.7
9  0.7            0.8
10 0.7            0.9
11 0.7            1.0
     a seq.0..1..0.1.
1  0.8            0.0
2  0.8            0.1
3  0.8            0.2
4  0.8            0.3
5  0.8            0.4
6  0.8            0.5
7  0.8            0.6
8  0.8            0.7
9  0.8            0.8
10 0.8            0.9
11 0.8            1.0
     a seq.0..1..0.1.
1  0.9            0.0
2  0.9            0.1
3  0.9            0.2
4  0.9            0.3
5  0.9            0.4
6  0.9            0.5
7  0.9            0.6
8  0.9            0.7
9  0.9            0.8
10 0.9            0.9
11 0.9            1.0
   a seq.0..1..0.1.
1  1            0.0
2  1            0.1
3  1            0.2
4  1            0.3
5  1            0.4
6  1            0.5
7  1            0.6
8  1            0.7
9  1            0.8
10 1            0.9
11 1            1.0

This does produce the kind of data points that I will need, however I need all these data points in one single data.frame instead of 11 because of further formatting I must do with the data.  Any suggestions?
Thank you,
Elysia