Tehnički glasnik, Vol. 7 No. 4, 2013.
Stručni rad
Chaotic behaviour in Newton iterative process approach - Newton’s fractal
Sanja Zlatić
orcid.org/0000-0002-8238-6001
; Veleučilište u Varaždinu, Varaždin, Hrvatska
Sažetak
Isaac Newton discovered what we now call Newton's method around 1670. Although Newton's method is an old application of calculus, it was discovered relatively recently that extending it to the complex plane leads to a very interesting fractal pattern. For equations that have more than one solution, the question is which solution will Newton's method lead to. Zeros of the observed function act as magnets for the iteration process and around themselves create the so called ‘attractive pools.’ The solution the method will find depends on the initial approximation. Graphically, each zero for given function is associated with a single colour, and the point of the complex plane are painted in the colour of the zero which they converge on. The boundary between the attractive pools is an extremely complicated subject. Although the pools themselves are not fractal because they contain large sets without any substructure, their boundaries have fractal properties. Starting from any point on the border of the pool, we always get the transition of iterative process into chaos.
Ključne riječi
approximation; iteration; Newton's fractal; Newton's method
Hrčak ID:
112056
URI
Datum izdavanja:
10.12.2013.
Posjeta: 1.919 *