Talk:Iterated function system: Difference between revisions

Revision as of 20:27, 15 May 2008

Revision as of 22:40, 15 July 2008

Line 83:

[[Image:Ifs-construction.png|thumb|right|400px|[[Ifs Construction]] IFS being made with two functions.]]

I propose adding the image on the right, with some text, possibly replacing the fern as the example. [[User:Spot|Spot]] 01:52, 30 May 2007 (UTC)

== Properties ==

Several things wrong here I fear.

* "In general, if there are p functions, then one may visualize the composition as a p-adic tree.". Link to [[p-adic]] takes you to p-adic numbers, not the same thing (see below), this is a ''full [[K-ary tree]]'' with K=p, ie each node has p immediate descendents.

* Confusion about the monoid (which consists of finite strings) and the tree (which has all infinite paths in it). The monoid can't consist of infinite strings, at least, not indexed by natural numbers: how could you compose the all L word with the all R word?

* Link to [[dyadic monoid]] redirects to [[modular group]], presumably intended to R to section Dyadic monoid. See [[Talk:Modular group]] for what I think is wrong there.

* "the elements of the monoid can be seen to be isomorphic with the p-adic numbers; that is, each digit of the p-adic number indicates which function is to be composed with." Not so. (1) The p-adic numbers form a ring, not a monoid. (2) the p-adic numbers have an infinite sequence of base p digits, the elements of the monoid are finite strings (3) the p-adic numbers are usually only defined for prime values of p (4) composition of finite p-ary strings is not isomorphic to either of p-adic addition or multiplication (5) the monoid is countable, the p-adic numbers are uncountable ...

* "The automorphism group of the dyadic monoid is the modular group". No, the automorphism group of the dyadic monoid is just the cyclic group of order 2. Proof. The monoid is generated by two elements L and R. The image of each under an automorphism must be a word of length 1 (otherwise the alleged automorphism would not be invertible) and so the automorphism is either L,R goes to L,R or R,L.

Would someone completely rewrite -- or delete -- this section please? [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 22:40, 15 July 2008 (UTC)