Hmmm...

the simple expedient of plugging the u-derived value into the y_index of the Noise node (instead of using a constant) makes all three planes render as hoped - but with a diagonal symmetry. And both FireFly and SuperFly render the same pattern.

 

But even better is using the v-derived value instead for the y_index input - no symmetry:

 

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The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident. And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU or something else.
*soon only to be available in two flavours -  DAZ and Renderosity