  Can machines design? Can they come up with creative solutions to problems and
build tools and artifacts across a wide range of domains? Recent advances in
the field of computational creativity and formal Artificial General
Intelligence (AGI) provide frameworks for machines with the general ability to
design. In this paper we propose to integrate a formal computational creativity
framework into the G\"odel machine framework. We call the resulting framework
design G\"odel machine. Such a machine could solve a variety of design problems
by generating novel concepts. In addition, it could change the way these
concepts are generated by modifying itself. The design G\"odel machine is able
to improve its initial design program, once it has proven that a modification
would increase its return on the utility function. Finally, we sketch out a
specific version of the design G\"odel machine which specifically addresses the
design of complex software and hardware systems. Future work aims at the
development of a more formal version of the design G\"odel machine and a proof
of concept implementation.
