Mandelbrot's negative dimensions and Lapidus' complex dimensions
have extended our concept of dimensions.
The isomers of the Moran dimension:
s=Log[2]/Log[7^(1/4)]=Log[4]/Log[Sqrt[7]]=Log[16]/Log[7]
suggest an extended Moran self-similarty form:
n^p/(m^p)^s=1
to give fractal rational integer Moran dimensions:
s[n_, m_, p_, q_] = N[Log[n^p]/Log[m^q]]
m<=2: m ratio
=m: n number of transforms
p and q integer or rational powers as q->1/q
When plotted this distribution of dimension has 2053 sequence values
between s=0 and s=25, for n,m<=10.
https://www.wolframcloud.com/obj/rlbagulatftn/Published/rational_Moran_Dimensional_sequence_both_q.nb
https://www.pinterest.com/pin/293648838212628366/
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)