I was thinking about the prototypes you showed me about understanding the concept of number. Inspired by that, and your principle of the learner controlling the educational artifact rather than the other way around, I made a prototype of a rectangle of numbers that you can adjust to see the periodicity patterns formed when there are different numbers of rows and columns, like so:

live demo (Chrome)

The idea is to hint at the structure behind the number system. Hint at the existence of a more powerful understanding of number that can be used to generate other concepts about number.

I also tried a version where each number is colored uniquely (kind of haphazardly).

But I think the arbitrary color obfuscates the structure, at least with the coloring system I made (which has periodic artifacts). Maybe adjustable color could be used to show a third periodicity.