Just thinking that the spiral groove on a record is a sort of space filling curve in the limit in polar coordinates... here dividing coefficients by 10 and going to 10*pi, the 10 could be forever increased to make the spiral denser...

If Maple had support for 3 dimensional parametric polar graphs, I could plot this where the z coordinate is following some kind of wave along the 2d spiral, here just sin(t)...

Then it would be like the surface of a record, with the height being the wave of the music to be played...

But we could also use it to construct a surface like...

Where the height of the red curve is the smoothest wave through the z values along the spiral, represented by the darkness and lightness in this graph...

Certain height maps, like one above, might be easier to represent this way than with other 3d surface interpolations like polynomial interpolation across a grid... I think the z coordinate of the one above would be a sine wave with decreasing frequency and increasing amplitude over time.. Things like spiral armed galaxies might be easy to describe... For other types of information different space filling curves might be more useful...

**Aside**

I was thinking about records and how much better of a musical record we could make nowadays with modern materials and engineering... like very hard ceramic coated high strength metal for the record and a high strength but slightly less hard material for a micro needle, so the grooves could be very close together for a very long playing record, and maybe with now adays electronic components it could be made so it also only needs to spin at very low rpm, making it play even longer... probably not practical but I always hear about vinyl coming back so maybe there would be some interest...

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