Complex and non-integer powers

[matsoljare]

There seems to be several different interpretations of complex powers, and non-integer powers applied to complex numbers. This application gives very different results for non-integer and complex powers than Ultrafractal does, for example, and there are examples of both kinds on Youtube. So which is the "correct" one? I'm more fond of this one, personally....

http://kawigi.yajags.com/showapplet.cgi?Complex+Fractal+Generator

[lkmitch]

The generator in the link appears to use an incorrect representation of raising a complex number to a complex power.  Mathematically, there is only one correct implementation (aside from the multiple values issue arising from the complex log being multi-valued); I'm fairly certain that Ultra Fractal uses it.  However, if you're primarily interested in images, it doesn't really matter.   

Kerry

[matsoljare]

<a href="http://www.youtube.com/v/3Zg3_J_jHCY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/3Zg3_J_jHCY&rel=1&fs=1&hd=1</a>

Here's a animated version of the "other way" of rendering non-integer powers. I much prefer this to the symmetrical one.