Thanks Lee! That is very exciting to read.
One of the last things he mentions is
which is equivalent to what I have as
\( a[x+1]b=[x]^{log_2 b}a \)
Somewhere in his OP he says it can be extended to real-argumented hyperoperators, but he never gets there as far as I can tell. He does plot a[4]a, which is really cool, and shows the fixed point at a=2.
There's a section on "Balanced hyperoperators" in the Wikipedia page. Apprently they were first considered in this paper.
One of the last things he mentions is
Quote:\( x[k+1]y={f_k}^{\circ (\log_2 y)}(x) \).
which is equivalent to what I have as
\( a[x+1]b=[x]^{log_2 b}a \)
Somewhere in his OP he says it can be extended to real-argumented hyperoperators, but he never gets there as far as I can tell. He does plot a[4]a, which is really cool, and shows the fixed point at a=2.
There's a section on "Balanced hyperoperators" in the Wikipedia page. Apprently they were first considered in this paper.