documentation about NEWTON-fractals from fractint.exe (19.2)
The Newton formula is an algorithm used to find the roots of polynomial
equations by successive "guesses" that converge on the correct value as
you feed the results of each approximation back into the formula. It
works very well -- unless you are unlucky enough to pick a value that is
on a line BETWEEN two actual roots. In that case, the sequence explodes
into chaos, with results that diverge more and more wildly as you
continue the iteration.
This fractal type shows the results for the polynomial Z^n - 1, which
has n roots in the complex plane.