Chaotic maps and pattern recognition - the XOR problem
Rogers, Alan and Keating, John G. and Shorten, Robert and Heffernan, Daniel M. (2002) Chaotic maps and pattern recognition - the XOR problem. Chaos, Solitions and Fractals, 14 (1). pp. 57-70. ISSN 0960-0779
In this report, we describe a novel application of the Baker's map. We demonstrate that the chaotic properties of this map can be used to implement basic operations in Boolean logic. This observation leads naturally to the possibility of new computational models and implementations for conventional computational systems. Here we show that by considering the variation of the fractal dimension of its attractor, and using varying parameter values as inputs, the generalised Baker's map can be used as a natural exclusive OR (XOR) gate. Further, this map can also be used to create other logical functions such as the AND gate. The efficacy of our results are demonstrated by means of a concrete application; namely by designing, to the best of our knowledge, for the frst time, a half-adder that is constructed entirely by utilising chaotic dynamics.
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