RESONANCE IN EN: M GROWTH-DECAY FRACTAL TIME FUNCTIONS

Abstract

There exists many kinds of fractal growth-decay En:m functions, depending on values for n and m. Equisegment En:m functions have immediate decomposition growth segments equal at all levels whereas regular En:m functions do not; both have the same decay fraction everywhere. A grodec stack machine whose pressure growth decay follows an En:m function is likely to be possible only for resonating functions. We have conclusively shown (a) that resonating equisegment E5:3 functions do not exist and (b) that a restricted family of resonating regular E5:3 functions does exist. A resonance equation for resonating regular functions is presented. It was discovered that there exists a simplest possible resonating regular E5:3 function satisfying the resonance equation. It is likely that a grodec machine for this simplest possible resonating function can be built. A controlling ratio within this function was found to be the Feigenbaum universal constant.