<programming> Repetition of a sequence of instructions.
A fundamental part of many algorithms.
Iteration is characterised by a set of initial conditions, an iterative step and a termination condition.
A well known example of iteration in mathematics is Newton-Raphson iteration.
Iteration in programs is expressed using loops, e.g. in C:
new_x = n/2; do x = new_x; new_x = 0.5 * (x + n/x); while (abs(new_x-x) > epsilon);
Iteration can be expressed in functional languages using recursion:
solve x n = if abs(new_x-x) > epsilon then solve new_x n else new_x where new_x = 0.5 * (x + n/x)
solve n/2 n
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Iterated Function System
conversion to iteration
cycle of reincarnation