NestList

NestList[f, expr, n] gives a list of the results of applying f to expr 0 through n times.

Examples

Create a list of successive applications:

NestList[f, x, 3]
(* {x, f[x], f[f[x]], f[f[f[x]]]} *)

Practical example:

NestList[# + 1 &, 0, 5]
(* {0, 1, 2, 3, 4, 5} *)

Please visit the official Wolfram Language Reference for more details.