Honestly, pretty awesome.
Suggestion:
Is there any way to create fractional bases with extra digits? [example: Base 1 1/2. We can have an extra digit to add [in this case, 2] to create numbers that aren't that messy.]
Decimal to Base 1 1/2 [extra digits]
0, 0
1, 1
2, 2
3, 20 [3 is represented as 20 since 3 is 2*1.5.]
4, 21
5, 22
6, 210 [6 is represented as 210 since 6 is (2*2.25) + 1.5, or 4*1.5]
7, 211
8, 212
9, 2100 [9 is represented as 2100 since it is 6*1.5]
Props for making this , this is immensely useful in looking into how it is possible for existing languages to naturally evolve, something I'm very interested in!!
If I remember right (it's been a long time since I made this), I did it that way because the part after the decimal point is what's interesting for this. If you're trying to compare integers, you can just compare them the normal way, and even fractions ≥ 1 you'd just compare the integer part and then compare the fraction part; this way it's slightly less typing if all the numbers are between 0 and 1.
I like this!!1!1!1 I do have a suggestion, can you try adding imaginary numbers? and same as the comment above me, trying to do less messy bases ( the ones that are already in the base form can still be used though, also this video might help. https://www.youtube.com/watch?v=PQAhC1M93C8&t=1069s)
another suggestion about octonions: since we're unifying i j in C and H, i think it's nicer to have k as "the one spanning octonions from quaternions" (exactly what cayley-dickson construction did), despite there's convention from quaternions that "ij=k". this way we could have i, j, ij, k, ik, jk, (ij)k as e1~e7. furthermore, it's ok to use ÿ as ij digraph that also avoids the necessity of parenthesis in (ij)k. then they become i, j, ÿ, k, ik, jk, ÿk.
bug report: entering 1/94906266, the denominator from this on, C, H jump out mysteriously...
and suggestion continued: for split complex (i'd rather call them hyperbolic), i think it's better to use "i'"=1 since it's completely different from i. also j'^2=ÿ'^2=1. and there's split quaternion using i' j or i j' together.... and (completely) hyperbolic quaternion i' j' ÿ' and so on... imo it's generally better this way.