The simulation of wood grain using solid texturing is not
easy. Between adding noise and turbulance there are many parameters
that need to be tuned before a reasonable model is achieved.
While the base model of concentric cylinders and the use of
cylindrical coordinates makes for a nice intuitive mapping to logs in
the real world. This model can yield poor results if the object is
allowed to be placed at large distances from the z-axis. This is
because as R increases the arc swept out be theta increases causing
effects such as birdseye to enlarge and blur.
Lastly as pointed out in  and evident from the model of birdseye,
realistic models of woods(especially figured woods) are dependent on
more than just the x, y, z coordinate. In addition to surface normals,
the vectors from the point to the light source and to the viewer would
be needed to capture the irredesence of many woods.