I did a search here to see if anyone had mad this portable and I found three threads which are from 2006 and can't accept comments which is why I am starting this one. I've seen some extraordinary fractals from this program and there is already a "portable" version available - see link:
http://sourceforge.net/projects/apophysis7x/files/
it would be very cool if some ambitious and talented developer made this in our favorite portable format.
thank you.