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iteration is the process of doing something over and over again. you start off with an initial value and plug it into a fuction, such as y=2x. the output of the function is equivilant to double the original value. in interation, the output is then plugged back into the function, and the process is repeated for a given number of times.

for example... if we iterated the function y=2x 5 times with an original value of 1, here's what would happen:

1. y = 2 x = 2 X 1 = 2
2. y = 2 x = 2 X 2 = 4
3. y = 2 x = 2 X 4 = 8
4. y = 2 x = 2 X 8 = 16
5. y = 2 x = 2 X 16 = 32

an area of study in iterations is end behavior. end behavior is how the function outputs behave... at the end. in other words, what would happen if we iterated something many times. sometimes the values will converge to one value. this is known as "convergence". another end behavior is bifurcation, or the "bouncing" of values from one value to another. end behaviors depend on the fuction and the initial value.

the logistic difference equation is a good way to show the different end behaviors of functions. different inital values will lead to different end behaviors. you can try it out by clicking on the link below.