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.
Notes
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