Mathematical Models of Computation Using Magnetic Bubble Interactions

Cylindrical magnetic domains in certain orthoferrite materials have been investigated extensively in recent years. 1-3 These domains, commonly referred to as bubbles, have the property that they can be moved within the material by the application of suitable external 1701 1702 T H E BELL SYSTEM TECHNICAL JOURNAL, J U L Y - A U G U S T 1971 magnetic fields. The motion of a bubble is also dependent on other bubbles in its vicinity. The locations of bubbles can be restricted to a finite set of possible positions in an orthoferrite platelet. The presence or absence of a bubble at a particular location may be treated as representing the values of a binary variable. Thus, magnetic bubbles seem to have natural applications in performing memory and logic functions. In a recent paper, R. L. Graham 4 considered the computational capabilities of a particular mathematical model of magnetic bubble interaction. The only type of interaction allowed in this model is represented by an instruction of the type (x, y) where x and y are distinct adjacent locations in the orthoferrite platelet. Application of this instruction results in moving the bubble in location x to location y if the latter does not contain a bubble prior to the application of the instruction. If x does not contain any bubble or y already has a bubble, no transfer of bubbles takes place. Two locations, only one of which contains a bubble, are used to represent each binary variable and its complement. Graham has shown that only a small fraction of all combinational functions of 11 or more variables can be computed by this model.