Cantor set/cantor dust and constructivism

Hello, This question is a little bit afield; however, it is still tied in with intuitionistic logic. On my Linux machine, I have a screensaver that is a three-dimensional of a Cantor set. A Cantor set has prescription or algorithm as to how we "calculate" or build it. Question: From a constructivist viewpoint though, can we ever realize the actual object which is infinite? Regards, Bill Halchin