  We study the q-dependent susceptibility chi(q) of a Z-invariant ferromagnetic
Ising model on a Penrose tiling, as first introduced by Korepin using de
Bruijn's pentagrid for the rapidity lines. The pair-correlation function for
this model can be calculated exactly using the quadratic difference equations
from our previous papers. Its Fourier transform chi(q) is studied using a novel
way to calculate the joint probability for the pentagrid neighborhoods of the
two spins, reducing this calculation to linear programming. Since the lattice
is quasiperiodic, we find that chi(q) is aperiodic and has everywhere dense
peaks, which are not all visible at very low or high temperatures. More and
more peaks become visible as the correlation length increases--that is, as the
temperature approaches the critical temperature.
