Who?

Superficially Charles looks, acts, sounds and juggles a lot like Boppo, although I'm not sure that's a Good Thing(tm).

My favourite Juggling Patterns

Messages

As of course you know, a good way to exhaustively search for length 3 SSNs is to start with:

• either 300 or 201, and then move up one ball by either:
  • add 111 to each, or 100/010/001 to each,
  • and then continuing.

0	.	.	.	.	.	.	.	.	.	.	.	.
1	300	.	.	.	.	.	.	.	.	.	.	.
2	411	600	330	.	.	.	.	.	.	.	.	.
3	522	711	441	900	630	603	.	.	.	.	.	.
4	633	822	552	.	741	714	930	903	660	.	.	.
5	744	933	663	.	852	825	.	.	771	960	906	.
6	855	.	774	.	963	936	.	.	882	.	.	990
7	966	.	885	.	.	.	.	.	993	.	.	.
8	.	.	996	.	.	.	.	.	.	.	.	.

201	.	.	.	.	.	.	.	.
312	501	420	.	.	.	.	.	.
423	612	531	801	504	720	.	.	.
534	723	642	912	615	831	804	750	.
645	834	753	.	726	942	915	861	807
756	945	864	.	837	.	.	972	918
867	.	975	.	948	.	.	.	.
978	.	.	.	.	.	.	.	.

&c &c.

Similarly, for Multiplex patterns, eg:

"adding" together the 3 permutations of 330 and 441 to give the 5-ball patterns: SS:[43][43]1 , SS:4[43][31] , SS:[43]4[31]

{of which only the 1st is easy - I find the others harder due to the [31]}

&c &c.

However, I've less experience of Synch patterns, so what would be an interesting algorithm of enumerating all (say) length 6 patterns?

Something like? {commas omitted to avoid keystrain}:

• (20)(20)(20)
• (22)(22)(22) (40)(40)(40)
• (42)(42)(42) (60)(60)(60)
• (44)(44)(44) (62)(62)(62) (80)(80)(80)

What might be a nice (numeric) way to go from pattern to pattern without having to draw ladders?

-- cab

See Inventing Synchronous Patterns. Still thinking about the modification methods for sync patterns. -- cdw

Still working on the bigger pages...

• PS. I like your site map. Maybe there's an isomorphism with each entry and AllenK's xxx-x-x diagram ?:-)
• PPS. I haven't tried your Dh shape - can I try it with my pupils next term?

• Re Site Map Expt: Thank you. There's also the original Site Map page.
• Still working on making the new version
  1. more readable
  2. more structured
• Re Paper Dodecahedron: Of course - let me know how it goes.

• Done a bunch of updates. Going to comment the remaining ones soon.

Quotation from Tim Berners-Lee