The idea came out of an attempt to represent numbers without having to choose an arbitrary base, i.e. an alternative to the place value system.
Just to be clear, this is an art project with no practical use that I can think of. It's hard to count using these numbers, but factoring them is trivial.
What logic does it use for when to use a +1? One thing I noticed: if I give it 100,000 it gives me 2^5•5^5. But if I give it 100,001, instead of 2^5•5^5+1, it gives (2•5 + 1)•(2•3^2•5•(2^2•5^2 + 1) + 1), which seems sub-optimal.
I don't get it. Is there a particular reason why prime number bases are further broken down via "+1"? And where do you stop with that? For example, "5" is not further broken down into 2^2+1.
It looks like powers of larger primes are currently rendered with the exponent ring overlapping the "main" rings, e.g. 7 and 49 look the identical, while 343 has an overlapping 2 and 3 knot.
Comments
The idea came out of an attempt to represent numbers without having to choose an arbitrary base, i.e. an alternative to the place value system.
Just to be clear, this is an art project with no practical use that I can think of. It's hard to count using these numbers, but factoring them is trivial.
What logic does it use for when to use a +1? One thing I noticed: if I give it 100,000 it gives me 2^5•5^5. But if I give it 100,001, instead of 2^5•5^5+1, it gives (2•5 + 1)•(2•3^2•5•(2^2•5^2 + 1) + 1), which seems sub-optimal.
It only uses the +1 for prime numbers. 100,001 is not prime.
This rule ensures that there is a unique representation for every number.
Fantastic! Thank you for explaining this.
Further down the prime numbers rabbit hole: you can do computation from prime numbers decomposition and fractions:
https://wiki.xxiivv.com/site/fractran.html
I don't get it. Is there a particular reason why prime number bases are further broken down via "+1"? And where do you stop with that? For example, "5" is not further broken down into 2^2+1.
Edit: Oh, have not seen the drawings...
Interesting idea.
It looks like powers of larger primes are currently rendered with the exponent ring overlapping the "main" rings, e.g. 7 and 49 look the identical, while 343 has an overlapping 2 and 3 knot.
True! Thanks for the bug report, I'll try to make the exponent rings larger.
Very slick interface and implementation! This is why I love coming to HN!
Thank you!
7 and 49 look the same.