Is all grid based noise inevitably anisotropic?
As usual with numerical methods and samplings, it also depends of your quality threshold of what you consider &quot;isotropic&quot;. And of what you would consider as a being or not a &quot;grid-based noise algorithm&quot;.
For instance Gabor Noise reproduces a target spectrum, for instance blue noise, which in Fourier domain is a simple isotropic ring.
Now if you consider that this ring is not analytic but rasterized, as such it is not perfectly symmetrical. Also if the ring radius (i.e., frequency) get too close to the window size (i.e., maximum frequency), it will be truncated (and thus no longer symmetrical). Up to you to accept or not these as anisotropic ;-)


&quot;This is not a circle&quot; - Magritte . . . . . . . . . . . . . . . .   &quot;This is not a circle&quot; - Nyquist
You might or might not accept a rasterized ring in Fourier space to be &quot;isotropic&quot;. Still, in the extreme cases where the ring get thinner than the resolution, or larger than the window, isotropy is objectively lost.