hi guys

first of all i would like to notice that many threads i started have one word and three exclamation signs.

second,i was just thinking about the many interesting iterations in mathematics and their use.

i know a few iterations,such as Newton's for finding roots of numbers,or the 196 iterarion used for finding if a number is a Lychrel number(none were proven to be such),and many more...

this has come to my mind when i was trying to do something like this:

let us have two actions represented by symbols a and b.

now if we take one of them,say a,than the other one,b,and then take both but in reverse order we get:
abba(which is also a group from sweden (i think!))

now we write that on a piece of paper.next we inverse it all(by substituting a for b and b for a) to get baab.we write that as well.now we write down both but in reverse order to get:

abba baab baab abba

now we repeat like in last two steps to get:

abba baab baab abba baab abba abba baab baab abba abba baab abba baab baab abba

you can continue to do this as long as you want,but when you are finished you can take a piano,or smth like that and take two notes for a and b.it sounds very boring but,hay,at least you know now how to spend 5 minutes of your time on nothing.

btw some geometric iterations are used to get the sierpinski's triangle or the apollonian gasket.

if you know anything about any iteration/iterations post it here.