OpenEuphoria

Dimension of sequences

• Posted by Fernando Bauer <fmbauer at ?otma?l.com> Sep 14, 2007
• 665 views

Hello All,

A basic question about sequences.

Suppose that a "retangular sequence" is a sequence generated by using
iteratively the function repeat() beginning with an atom. Then, I think we can
say that the dimension of a retangular sequence is the number of calls to
repeat() function. (atom=dimension 0, vector=dimension 1, matrix=dimension 2,
...).

Now, let's say we have a sequence like { 1, {1,1} } which is not retangular.
Then, a question arise:

What is the dimension of a non-retangular sequence ?

a) the maximum depth of the sequence.
b) an integer number.
c) a fractal number.
d) a sequence which depends on the structure.
e) the dimension concept does not apply.
f) I don't know.
g) other.

Trying to answer that question, others more basics and related to that arise to
me (sorry if they are stupid!):

What is the dimension of the circumference ?
a) 1 , because the area of the circumference is zero. It is a curved 1D object.
b) 2 , because the circumference exists in a bidimensional space.
c) Both. It has 2 types of dimensions!

Same question for a line not closed as, for example, the form of letter "U".

Thanks for your reply,

Regards,
Fernando Bauer