EN:M FRACTAL TIME FUNCTIONS, GRODECS AND GRODEC STACK MACHINES
Date
1995-12-01
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Abstract
This paper is concerned (a) with a family of fractal growth-decay
time functions called En:m functions, (b) with fundamental
growth-decay storage and switching components called
grodecs, that have the switching properties of neurons, and
(c) with machines constructed from stacks of grodecs, called
grodec-stack machines. An En:M function consists of a series of
replicating and endlessly subdivided alternating growth and decay
segments. Grodecs could be used to build computing machines that work
like biological information processing organs but that aspect of grodec
machines is not analysed. The grodec stack machines presented and
analysed exhibit time fractal growth-decay En:m function behaviour.
Left-sink grodec-stack machines can exhibit En:1 function behaviour
where only growth segments subdivide, and right sink grodec stack machines
can exhibit negative En:1 function behaviour where only decay segments
subdivide. These two types of machines can be combined to form
balanced grodec-stack machines with En:m function behaviour - where
both growth and decay segments subdivide. It is shown that only
resonating En:m functions can be generated by such machines. The
behaviour of grodec stack machines can be unfathomably complex; they can
exhibit sensitive dependence on initial conditions, and therefore also chaotic
behaviour.
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Computer Science