Abstract
As is well known, iterated function systems are time discrete maps whose image can give rise to fractal-like point sets [l]. These noninvertable sets may or may not converge towards some orderly or disorderly looking pattern. Familiar examples for such patterns are the Sierpinski gaskets and Sierpinski carpets [2]. It is this property of being able to generate chaotic or orderly looking points as time passes which suggested to us that these maps in which randomness plays a key role, may be analogous to or in fact mimic the famous two-slit interference experiment with photons or other particles obeying the rules of conventional quantum mechanics [3]. In what follows we would like to draw attention to an informal but instructive analogy between iterated functions in the sense of Hutchinson [l, 21 and the two-slit experiment which we think may be quite valuable in illuminating the role played by the possibly DNA-like Cantorian nature of micro spacetime [4] and clarifying the way in which probability enters into this subject. The suggested analogy may be subdivided into three parts as follows.
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