Indeed. You could map it somewhat using a computer in 3D + Time, which is 2 more dimensions to work with, but beyond that, it’s diminishing quality, shadows of shadows of shadows of higher dimensions.
One way to sneak a FEW more dimensions into visualizations is to take advantage of colorspaces, representing each higher dimension by a color, or a particular width of a line, or by a rotation or a zoom.
But while you’ll end up with a pretty thing, how much it actually represents the pattern is iffy.
I think if I had to do it, I’d do it in a first person tunnel with branching tunnels.
You’d see the omega(n) at each dimension but only make a single turn into a higher dimension. In that tunnel, you’d see the next and so on.
This sense of traveling might bring part of the awe to a viewer.
Very cool read. I love how he used his system to programmically generate math formulas and proofs just as easily as one another.
I would have preferred a NOR gate than a NAND, as NAND is serial and NOR is parallel, but NAND is flatter and easier to represent visually – and they’re both universal circuit makers.
But what a clever use of it!