  Generalizing the previous works on evolving fuzzy two-sphere, I discuss
evolving fuzzy CP^n by studying scalar field theory on it. The space-time
geometry is obtained in continuum limit, and is shown to saturate locally the
cosmic holographic principle. I also discuss evolving lattice n-simplex
obtained by `compactifying' fuzzy CP^n. It is argued that an evolving lattice
n-simplex does not approach a continuum space-time but decompactifies into an
evolving fuzzy CP^n.
