GRODEC STACK MACHINES FOR GENERATION OF EN: 1 GROWTH-DECAY FRACTAL TIME FUNCTIONS

Abstract

This paper analyses machines that exhibit time fractal growth-decay En:m function behaviour. It is largely concerned with the simpler types of En:m functions, namely the E5:1, E5:3, E7:1, E7:5 functions. An En:m function consists of replicating and endlessly subdivided series of alternating growth and decay segments. The machines involved are grodec stack machines, constructed from entities called grodecs. A grodec is a basic growth decay entity involving two stores of fluid and energy, connected via a one way switch. Grodec stack machines can be built from two kinds of grodecs, namely left sink grodecs and right source grodecs. This paper analyses four classes of grodec stack machines: left sink grodec stacks for equisegment En:1 functions and regular En:1 functions, and right source grodec stacks for negative equisegment En:1 functions and negative regular En:1 functions. Negative En:1 functions are fractal time functions that grow downwards. It appears that a machine for generating an En:m function with m > 1 is a combination of left sink and right source grodec stack machines, called a balanced grodec stack machine. Such a machine can also be called a chaos machine because of its sensitive dependence on initial conditions, and capacity for chaotic behaviour.