"Empty space" computes

Abstract

Lee A. Rubel defined the extended analog computer to avoid the limitations of Shannon's general purpose analog computer. Partial differential equation solvers were a "quintessential" part of Rubel's theoretical machine. These components have been implemented with "empty space," or VLSI circuits without transistors, as well as conductive plastic. For the past decade research at Indiana University has explored the design and applications of extended analog computers. The machines have become increasingly sophisticated and flexible. The "empty" computational area is devoted to solving partial differential equations. The rest of the space includes fuzzy logic elements, configuration memory and input/output channels. This paper describes the theoretical definition, architecture and implementation of these unconventional computers. Two parallel applications are described in detail. Rubel's model can be viewed as an abstract specification for a distributed supercomputer. We close with a description of an inexpensive 64-node processor that was designed using our current single processor. The next step is to return to VLSI with an improved understanding of the architecture-and seek computation speeds approaching trillions of partial differential equations per second.