0.00110  & 91.60534  \\
 90  &       0.99990  &       6.00000  &      15.00088  &      20.00156  &  0.00018  & 89.78209  \\
100  &       0.99998  &       6.00000  &      15.00014  &      20.00025  &  0.00003  & 87.95883
\end{array}$$

We finish the Riemann sphere case with a visual example of Donaldson’s $T$-iterations. We choose a palindromic metric which we can realize as induced from an embedding of $\mathbb{CP}^1$ into $\mathbb{R}^3.$ In particular we pick $$G = (1, 300, 300, 300, 1)$$ on $\mathrm{H}^0(\mathbb{CP}^1, O(4)),$ which is a metric obtained if one where to pinch the sphere around two latitudes giving it two narrow necks. See figure \[plot0\].

![$\mathbb{CP}^1$ with metric induced from $G = (1,300,300,300,1).$[]{data-label="plot0"}](plot0_gray.eps){width="1.5in"}

Now, in figure \[The iterations\] we plot the evolution of the metric $G$ under the iterations of $T, T_K$, and $T_{\nu},$ respectively.

\
![The first four iterations.[]{data-label="The iterations"}](plot0_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotT1_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotT2_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotT3_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotT4_gray.eps "fig:"){width="\wid"}\
![The first four iterations.[]{data-label="The iterations"}](plot0_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotTK1_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotTK2_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotTK3_gray.eps "fig:"){width="\wid"} ![The first four iterations.[]{data-label="The iterations"}](plotTK4_gray.eps "fig:"){width="\wid"}\
![The first four iterations.[]{data-label="The iterations"}](plot0_gray.eps "fig:"){width="\wid"} ![The first four 