I- 5- 5 Potenzieren mit – i – Seite 5 — To the Power of -i – (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 from the author, he was excited to find such ‚combined‘ functions in the articele Lit(2) . We have used those intensly and we have the strong feeling that they are rarely found in literature except log(cos) and log(cosh) as solution of integrals of tan and tanh.

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 .