Potenzieren mit – i – Seite 5 — To the Power of -i – page 5 (Some Functions inspired by Cleve Moler, Matlabwork)

This page partly was inspired by an article published by Cleve Moler, Mathworks, (Lit2), http://de.mathworks.com/company/newsletters/articles/GPU-Enables-Obsession-with-Fractals.

As a personal comment the author has found such ‚combined‘ functions for the first time in the articele obove. We have used them intensly and we have the strong feeling that they are rarely found in literature.

Starting point was the function f(z) = tan(sin(z)) – sin(tan(z)) . It was used by Cleve Moler to create an extremely attractive complex fractale.

Abb.: I-5-5-1 tan(sin(z) – sin(tan(z) , k=0:1 ( 1 repetition).
Abb.: I-5-5-2 f = (tan(sin(z) – sin(tan(z) ),- ^i .
Abb.: I-5-5-4 f = tan(sin(z) – sin(tan(z) ) , Iteration-2, ^i, (16*10^6 pixel). (Iteration-2 stands for twofold application, see page I-5 Introd.



Abb.: I-5-5-7 f = (tan(log( z ^-3) – log(tan(z ^-3))), – ^i .


Obsession with complexity .

Abb.: I-5-5-8 f = log(z*cos( z ^2)) , Iteration-4 , – ^i .
Abb.: I-5-5-9 f = log(z*cos(z ^2)), Iteration-4, repetition k=0:2, -^i .
Abb.: I-5-5-10 f = z*log(z*cos( ^3), -Iteration-3 , -^i .
Abb.: I-5-5-12 f = z*log(sin( z ^2)) , Iteration-4, -^i .
Abb.: I-5-5-13 f = z*log(sin( z ^3)) , Iteration-4 , – ^i .
Abb.:-I-5-5-14 f = z*sin(z ^3) , Iteration-4, then five times (k=0:4) executed , -^ i .
Abb.: I-5-5-15 f = log(z ^ cot(z))-Iteration-4, -^ i .
Abb.: I-5-5-15a f = log(z ^ cot(z))-Iteration-4, -^i , enlarged by factor 2 .