There was a nice bonus on my construction for a Continuous Extension for the HyperPower operator, which I discovered only two days ago. The definition that I use, seems to produce an infinity of new shapes if one traces the hyperexponent continuously. For example, although (-1)^^n = -1, for all n in N, (so that the function (-1)^^y returns infinately often to -1) the behavior of (-1)^^y for values in between natural numbers appears to be quite complex. A couple of .GIF trace samples, along with a short cross-referenced indirect proof that lim[n->+oo]i^^n exists (by considering the traces of i^^y, y>=0), can be found at: <[URL]http://users.forthnet.gr/ath/jgal/math/exponents4.html#trace>[/URL] in my Math section: <[URL]http://users.forthnet.gr/ath/jgal/math/>[/URL] Enjoy the read.