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What's 8 plus five (in digits only)?

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File: CharlesBrookman

!! Who?
Charles Brookman independently invented the SiteSwap notation.
He has juggled seven balls, although is a little rusty, and
has worked on nine, with mixed success.

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

----
!! My favourite JugglingPatterns
As and when I get a chance I'll annotate my favourite juggling
patterns.  These aren't all possible SiteSwaps, only the ones
I think are of interest or value.  This is a work in progress.
********>
  * SiteSwapsWithOneBall
  * SiteSwapsWithTwoBalls
  * SiteSwapsWithThreeBalls
  * SiteSwapsWithFourBalls
  * SiteSwapsWithFiveBalls
********
  * SiteSwapsWithSixBalls
  * SiteSwapsWithSevenBalls
  * SiteSwapsWithEightBalls
  * SiteSwapsWithNineBalls
  * SiteSwapsWithTenBalls
********<

----
!! Messages
A question:

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.
So, eg

| 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)

But then the x's?

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

-- cab

See InventingSynchronousPatterns. 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?

-- cab

* Re SiteMapExpt: Thank you.  There's also the original SiteMap page.
  * Still working on making the new version
    1 more readable
    1 more structured
  * Re PaperDodecahedron: Of course - let me know how it goes.

-- cdw

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

-- cab