> 
# maporbit.ms
# Iteration of 1-Dimensional Maps
> maporbit := proc(F, x0, skipiter, displayiter)
>    local x, k, c, orbit;
>    x := x0; # starting value
>    # skip some iterations before collecting points
>    for k from 1 to skipiter do x := F(x); od:
>    orbit := array(1..displayiter,1..6);
>    for c from 1 to 3 do
>       for k from 1 to displayiter do
>          orbit[k,2*c-1] := skipiter+(c-1)*displayiter+k-1;
>          orbit[k,2*c] := x;
>          x := F(x);
>       od:
>    od:
>    op(orbit);
> end:
# Can also convert to a list for more convenient processing if  desired.
> orbitlist := proc(orbit)
>    local i, j;
>    seq( seq( [orbit[i,2*j-1],orbit[i,2*j]],
>       i=1..linalg[rowdim](orbit)), j=1..3);
> end:
# Test the procedure on the logistic map
> Q := (x) -> a*x*(1-x):
> a := 2.9: maporbit(Q, 0.1, 1000, 10);
> a := 3.2: maporbit(Q, 0.1, 1000, 10);
# Test sensitivity to initial conditions
> a := 3.2: maporbit(Q, 0.1, 10000, 10);
> a := 3.2: maporbit(Q, 0.100001, 10000, 10);
# Test sensitivity to initial conditions
> a := 3.9: maporbit(Q, 0.1, 10000, 10);
> a := 3.9: maporbit(Q, 0.100001, 10000, 10);
>