The mathematical definition of the Mandelbrot set is:
z <— z ** (squared) + c
An iteration is the repetition of a mathematical operation on each term of a series, according to a formula to generate its next term.
For instance, the series 1, 2, 3, … is generated by the formula
n’ < n + 1
(That’s another of many alternative ways of expressing a formula in text.)
For the Mandelbrot Set’s formula, z and c are complex numbers.
(A complex number is a number of the form a+bi, where a and b are Real numbers [I can’t get “are Real numbers” (or this) to be Normal size.], and i is the square root of -1.)
(A Real number is simply the numbers that we are familiar with, such as 1, and 2.32.)
(So z_n**2 + c works out to be
(a_n + b_ni)**2
=
a_n**2 + 2abi – b_n**2)
A point is called “stable” under an iteration Formula if the series produced by an unlimited number of iterations of 0 is bounded (ie, remains finite)
(as opposed to increases without limit (aka “escapes to infinity”)).