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 [1] 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.