Elias Mårtenson on Nostr: Here's one of those interesting posts by Greg Egan which talks about some interesting ...

Here's one of those interesting posts by Greg Egan (npub12cu…d38p) which talks about some interesting properties of hexadecimal numbers: https://mathstodon.xyz/@gregeganSF/114489111257308697

I wanted to play around with this myself, and since I used Kap to do it, I just wanted to share what this looks like. Here's the original list of numbers, computed from first principles by splitting up each number into a binary array, performing the shifts, grouping the bits in groups of 4, encoding each group in binary and then encoding each group in base 16: [example](https://kapdemo.dhsdevelopments.com/clientweb2/#c=aW86dG9IZXjCqCAxNuKKpSAy4oql4o2JIOKKgyg2NOKNtDEgMCAwIDApIOKKhiDiioMgKOKNszUpIOKMvcKoIOKKgiAoNjTijbQyKSDiiqQgMHhhZjlkMDNjNmJlMjE1NzQ4 )

It could have been shorter if I had encoded the entire number in binary first, but I didn't do that because what I actually wanted to do was to work with the groups of 4 bits to show the symmetry where each group adds up to 8. Here's the code to do this: [example](https://kapdemo.dhsdevelopments.com/clientweb2/#c=Ky9bMV0g4oqDICg2NOKNtDEgMCAwIDApIOKKhiDiioMgKOKNszUpIOKMvcKoIOKKgiAoNjTijbQyKSDiiqQgMHhhZjlkMDNjNmJlMjE1NzQ4 )

The output is as follows:<code> +/[1] ⊃ (64⍴1 0 0 0) ⊆ ⊃ (⍳5) ⌽¨ ⊂ (64⍴2) ⊤ 0xaf9d03c6be215748<br>┌→──────┐<br>↓8 8 8 8│<br>│8 8 8 8│<br>│8 8 8 8│<br>│8 8 8 8│<br>│8 8 8 8│<br>└───────┘<br></code>

If you change the value to a number which doesn't have the symmetry mentioned in the post, the array will not be all the same number.

#maths #kap #apl