big planet: all spheres (assuming the planet is modeled as a sphere) are equivalent to the unit sphere. So not an example..size doesn't matter.

In theory you are right. But in the context of IEEE 754 where we have discretized floating point values, you are not.

Here, the equivalency breaks.

A planet - even with a 2D-parameterization of space (longitude-latitude, two angles) - is exactly equivalent to mandelbrot, with all the same problems involved. And that problem is:

*with any fixed-length (in number of bits, that is) numerical representation like IEEE 754, there is no and cannot be any parameterization of the surface of a sphere (any sphere) that lets you reach every point on the sphere. You can only advance on the sphere surface in discretized steps.*As you said rightly, size does not matter, but

*precision does*!

So, simply put: you cannot increase the size of your planet indefinitely (or normalize it back again to unit size indefinitely) while still keeping the same unit of length say 1mm and still want 1mm resolution of small notches and rocks and hills on your planet.

So, because magnitude does not matter, it all depends on the order of magnitude you choose as your basic unit of length. Of course, if you choose 1 meter instead of 1 mm you can scale down the sphere by another factor of 1,000 while still retaining the desired precision (namely now 1 meter).

EDIT: Plus: I did not make this up as a contrived text-book example. It exists in real-world. A big world, by the way