User blog comment:Simplicityaboveall/Insanely Fast-Growing Functions/@comment-1605058-20170915175750/@comment-28606698-20170922082324

Indeed, in slow growing hierarchy to reach $$g_{\omega^2}(10)$$ we should come through 100 ordinals starting with zero and that is why $$g_{\omega^2}(10)$$ is just 100, but it is not right for fast growing hierarchy.

For calculation of $$g_{\omega+1}(10)$$ we should come through $$\approx10\rightarrow10\rightarrow10\rightarrow2$$ ordinals starting with zero.

For calculation of $$g_{\omega2+1}(10)$$ we should come through $$\approx10\rightarrow10\rightarrow10\rightarrow10\rightarrow2$$ ordinals starting with omega.

For calculation of $$g_{\omega3+1}(10)$$ we should come through $$\approx10\rightarrow10\rightarrow10\rightarrow10\rightarrow10\rightarrow2$$ ordinals starting with omega2.

And so on.