>>105
Let us start to use proper terminology so that we can define it all appropriately.
[m]1: f
n(
x) defines an iterated function in degree
n.
x1 = f(
x0) = f
[sup]0(
x)
x2 = f(
x1) = f
[sup]1(
x)
x3 = f(
x2) = f
[sup]2(
x)
...
xn+1 = f(
xn) = f
[sup]n(
x)
[/m]
If strands
begin at holes, then there are just as many strands as there are holes... a part of a strand defined as an output
y that cannot be reached for f
n(
w) for
n <
N.
Therefore, the set of all strands (being a set of vectors of dimension
N at most) is the set
A -
C.
where
A:
f
n(
X)
set of all possible unique cycles
and
C is equal to
A, taking away all the elements that have a vector
c0 = {v
1, v
0, ... v
n} where
v1 is a unique value in the vector. It's likely that all other vectors are either combinations of these vectors, or have some complementary properties with other vectors that could be discerned.