Can anyone explain function iterations in a simple way?

Question

What is a function iteration exactly? How does it relate to fractals?
Exactly how to graph a simple one such as y=0.5x + 3? Finally, how to tell if it's attracting, repelling, etc. And what is the attracting/repelling point?

Please help me!!! Thank you all if you answer!

Answer 1

A function iteration in the simplest terms is a function which contains an incremental "n", such as n+1 in a series. Iteration is repeating a set of rules or steps over and over. One step is called an iterate.
Fractals are created by some specific (usually complicated) iterative functions.

The function you gave doesn't seem to be iterative (it is just linear), was something missing?

Answer 2

y=o.5x+3 For x use the numbers 0,1,2,3,4,5,6
y=3,3.5,4,4.5,5,5.5,9

Then you need to use graph paper and plot the points on the x and y coordanants. starting at( x=0,y=3.) (x=1,y=3.5)etc.then you need to draw a line from point to point. I do not have a math book to explain the attracting or repelling part of this problem. I hope that some one can explain it for you.

Answer 3

The .each and every approach takes a functionality as a parameter and calls it countless circumstances. each and every time the functionality is termed, a sparkling set of variables declared in that functionality is created. That functionality creates 2 new applications each and every time that's administered. those applications communicate with the variables of the functionality they have been declared in. while the outer functionality finishes, the variables that it declared nevertheless exist (closure), and the internal applications communicate with them. while the outer functionality is administered for the subsequent element, a sparkling set of variables is created, a sparkling pair of handlers is created, refering to the recent occasion of src, and absolute to the image element. So one functionality gets called diverse circumstances each and every time that's named a sparkling set of variables is created 2 new applications are created in the process the call the applications communicate with the variables of that decision, long after the call itself has ended. the certainty that variables can outlive their defining functionality helps using closures, that are the scopes of the variables after the linked functionality call has ended.

Answer 4

Maybe this will help http://en.wikipedia.org/wiki/Function_iteration