at late time.

![The extent of space $R^{2}(t)$ is plotted against $t$ for the typical solution with $N_{\rm X}=64$ and the block size $n=10$. []{data-label="fig:R2"}](R2.eps){width="10cm"}

Next we define a $3\times3$ real symmetric tensor $$T_{ij}\left(t\right)=\frac{1}{n}\mathrm{tr}
\left(\bar{X}_{i}\left(t\right)\bar{X}_{j}\left(t\right)\right) \ ,$$ whose eigenvalues $\lambda_i(t)$, which we order as $\lambda_{1}(t) \leq \lambda_{2}(t) \leq \lambda_{3}(t)$, represent how the 3-dimensional space extends in each direction. Note that they are related to the extent of space $R^2(t)$ as $$R^{2}\left(t\right)=\sum_{i=1}^{3} \lambda_{i} (t)  \ .$$ In Fig. \[fig:T\], we plot the eigenvalues $\lambda_i(t)$ for the typical solution discussed above. The three eigenvalues $\lambda_i(t)$ turn out to be roughly equal at each time. We have also confirmed that the three eigenvalues tend to come closer to each other as one increases the matrix size $N_{\rm X}$, suggesting that the SO(3) symmetry is recovered in the limit of infinite matrix size.

![The eigenvalues $\lambda_i (t)$ of $T_{ij}(t) \ (i,j=1,2,3)$ are plotted against $t$ for the typical solution with $N_{\rm X}=64$ and the block size $n=10$. []{data-label="fig:T"}](EV_Tij.eps){width="10cm"}

![The eigenvalues of $Q(t)$ are plotted against $t$ for the typical solution with $N_{\rm X}=64$. There are ten of them reflecting the chosen block size $n=10$. []{data-label="fig:Q"}](EV_Q.eps){width="10cm"}

In order to probe the structure of the 3-dimensional 