User blog comment:GamesFan2000/Extended E-star(E*) Notation/@comment-4852660-20181211115942

Excellent work. The funny thing is, I was actually working on an array notation for the E* function myself, haha! I believe this version is faster growing than the base of my notation, but I tried extending the arrays into the "3rd  (and possibly higher) dimension", if you will, lol. Basically, I defined:


 * Define K  as the last entry in an array, K-1 is the 2nd-to-last, etc.
 * Define R as the "realm" or "dimension" level

= E*[0](x,y,z,w, ... ,K-2,(E*[0](x,y,z,w, ... ,K-2,  .  .  .  . (E*[0](x,y,z,w, ... ,K-2,K-1))))  .  .  .  . )))
 * E*(x,y,z, ... ) = E*[0](x,y,z, ... )
 * E*[0](x,y) = E*(E*(E* . . . (E*(x))) . . . )) --where there are y amount of E*s
 * --where there are y amount of E*[0]'s/iterations
 * E*[0](x,y,z) = E*[0](x,(E*[0](x,E*[0](x, . . . (E*[0](x,y))) . . . )))
 * --where there are z amount of E*[0]'s/iterations
 * E*[0](x,y,z,w, ... ,K-2,K-1,K)
 * where there are K amount of E*[0]'s/iterations

This is how I defined it, but I might use your way of extending E*(x) if that's alright, since I believe it's faster growing than mine. Either way, we can continue adding +1 to R by using these rules:


 * E*[R](x,y) = E*[R-1](x,x,x, ...) where there are y amount of x's
 * E*[R](x,y,z,w, ... ,K-2,K-1,K)
 * = E*[R](x,y,z,w, ... ,K-2,(E*[R](x,y,z,w, ... ,K-2,  .  .  .  . (E*[R](x,y,z,w, ... ,K-2,K-1))))  .  .  .  . )))
 * where there are K amount of E*[R]'s/iterations

So, some examples: = E*[1](x,y,z,w, ... ,K-2,(E*[1](x,y,z,w, ... ,K-2,  .  .  .  . (E*[1](x,y,z,w, ... ,K-2,K-1))))  .  .  .  . ))) = E*[2](x,y,z,w, ... ,K-2,(E*[2](x,y,z,w, ... ,K-2,  .  .  .  . (E*[2](x,y,z,w, ... ,K-2,K-1))))  .  .  .  . ))) etc.
 * E*[1](x,y) = E*[0](x,x,x, ...) where there are y amount of x's
 * E*[1](x,y,z,w, ... ,K-2,K-1,K)
 * where there are K amount of E*[1]'s/iterations
 * E*[2](x,y) = E*[1](x,x,x, ...) where there are y amount of x's
 * E*[2](x,y,z,w, ... ,K-2,K-1,K)
 * where there are K amount of E*[1]'s/iterations