# Apply Functions Iteratively

I have a few functions `R1,R2,R3,R4`

which act on vectors. If `X = matrix(3,1,(x0,y0,r))`

then I have `R2`

defined as

```
def R2(X):
return matrix(3,1,(-X[0,0],X[1,0],X[2,0]))
```

For instance, if `v = matrix(3,1,(1,1,1))`

, then applying R2 to v gives the matrix $(-1,1,1)$.

I'd like to apply about 10 "levels" of iteration of these functions and have the output as a list of vectors. So, the list should be $R1(v), R2(v),R3(v),R4(v),R1^2(v),R2(R1(v)),R3(R1(v)),R4(R1(v)),R1^3(v),...,R1^{10}(v)\,...,R4^{10}(v)$ (as vectors) where $R_j^n = R_j \circ \cdots \circ R_j$ $n$ times.

How can I do this?