Which nodes work and which of x,y,z the constant should be plugged into cropped up again here Using 3D nodes (Cellular) with 2D UV maps ? and are, to are large extent, now understood.

Ish... ;o)

It's the same as the most recent screenshot except that what's plugged into the y_index input of the Noise node has changed, and now unused node that was plugged in has been deleted. I also changed the number of tiles and the mortar thickness.

Set Value_1 of Math_Functions on the right to the number of tiles you want, but don't change anything else in the three columns of nodes at the right. You can change the colour/value of any parameters in the Noise, ColorRamp and Tile nodes that don't have an anything plugged into them. The x_index, y_index, and z_index values in the Noise node and the Mortar_Thickness in the Tile node are fair game too.

FireFly and SuperFly renders again. You can see those artefacts I mentioned in the FireFly render again - definitely similar to what I spotted back in Aug 2019

I can't attach mt5 or txt files to this post, but I plan to upload the shader here in Renderosity's FreeStuff

Okay, that seems to work on the toon pool too, albeit there's a minor artefact on the FF render now (just to the right of the diving board, a sort of vertical line) - I think I can live with that

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:

"Oh my giddy aunt" and other expletives !

Yes, I clearly had a sneaking suspicion back in Aug 2019...

Just created four perpendicular planes aligned with x, y, and z axes, each mapped to the full UV square and applied my random pool tiles material.

FireFly has no problem:

SuperFly on the other hand - if the constant is plugged into the y_index input of the Noise node (with the u/v derived values plugged into the x and z), as in my shader, the XZ plane is okay but the other two aren't.

Plug the constant into the x_index, with u/v to y/z:

And constant to z_index:

Exasperated. That's a good word for how I feel.

...and the final step, apply that to the toon pool I'm working on..

FireFly looks great, but uh-oh, what's up in SuperFly ? The sides of the pool show very little variation.

FireFly:

SuperFly:

Adding the ColorRamp and Tile nodes as before, but also increasing the grid to 20x20...

FireFly:

SuperFly:

Looking good !

Almost there...

But the Turbulence and Cellular nodes don't seem to work here.

So in summary:

I've given the Noise node a double tick because it's easier to get a good dynamic range (near black to near white) than with fBm and Fractal Sum which always seem to give me justa small dynamic range of greys.

(the other 3D nodes don't have x/y/z scale inputs and thus aren't relevant here)

Fractal Sum node with default settings, FireFly render:

Fractal Sum node with default settings, SuperFly render:

Okay, after a good night's sleep I'm now wide awake... comparatively.

Just confirmed that using the Noise or Fractal Sum nodes instead of the fBm node also works, in both FireFly and SuperFly renders. It's just the node preview in SupeFly that looks wonky. Here's some screenshots showing the node preview and render together. The cropped nodes to the right are the same as before, just to create that 8x8 grid.

Noise node with default settings, FireFly render:

Noise node with default settings, SuperFly render:

A quick spreadsheet check indicates a max error of around 0.001° for your approximation, compared to 0.1° for the one I used. Nice one ! :o)

Plugging the fBm into a ColorRamp to convert the greys to colours, and then plugging theat into a 2D Tile node to get the grout/mortar between the pool tiles (that seemed the simplest way)...

FireFly:

SuperFly:

Yes, I'm trying to do that random blue swimming pool tiling. 

Hmmmm... the fBm node is the only node that seems to work for me. 

Here's a screenshot of a simple shader (based on the screenshot in this post from that 'PP2014 Image Map Node...' topic mentioned above, but modified to create an 8x8 grid) with a  FireFly render. The second (unconnected) fBm node is a duplicate of the connected one and has all the same values:

If I leave the material room, change the renderer to SuperFly, and go back to the material room (exit/re-enter required to update the mat room preview) the preview of the connected fBm node looks unpromising, but when I render it seems to work okay:

(I'll do the same with the other nodes tomorrow)

That's the beauty of compound nodes - they hide all the spaghetti! 😁

I've found one of the bits I was thinking of - from bagginsbill's post on my 'PP2014 Image Map Node: V_Offset = (V mod 0.03125) - V ...unexpected result' topic onwards

(I need to get a good night's sleep, my brain's leaking again ;o) )