# apply functions iteratively (modified re-post)

*(This is a modified re-post of Apply Functions Iteratively since my original question wasn't answered)*

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

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

then I have

```
def R1(X):
return matrix(3,1,(X[0,0]/(X[0,0]^2+X[1,0]^2-X[2,0]^2),X[1,0]/(X[0,0]^2+X[1,0]^2-X[2,0]^2),X[2,0]/abs(X[0,0]^2+X[1,0]^2-X[2,0]^2)))
```

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

```
def R3(X):
return matrix(3,1,(-X[0,0]+2,X[1,0],X[2,0]))
```

```
def R4(X):
return matrix(3,1,(X[0,0],-X[1,0]+2,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.

I know how to apply a single function iteratively, but I don't know how to combine/loop the four together. Thanks.