Hyperoperation visualization

Thomas Lamb

Click to cycle through different slices of n.

This is a visualization of hyperoperation. In broad strokes, hyperoperation is what you're talking about when you ask "what comes after addition, multiplication, and exponentiation?"

What is being plotted

There are four variables in question. The operands u, m, and result r:

u + m = r
u × m = r
u m = r

And n, which indicates the "level" of the operator:

1+
2×
3^

Why?

This is just for fun. Here are some remaining challenges:

  1. Generalize the operands to the set of reals
  2. Generalize the algorithm to allow for different identities
  3. Calculate the values of mathematical constants with different identities. Look at the forms of famous formulae with different identities. For example: is e = -1 still true when identities for its operators are different? If not, what does it look like given an arbitrary set of identities?