Rotation

From JuggleWiki

Site-swap code, along with its pattern, is assumed to continue as an endless loop:
123123123123....      1234123412341234....      123451234512345....

From this, it is assumed that a code string could be written from any starting point:
231 or 312;      2341 or 3412 or 4123;      23451 or 34512 or 45123 or 51234

The term "rotation" refers to visualizing that principle as a clock-wise loop:

1 2 3          1 2 3 4            1 2 3 4 5
  1               1                   1
3   2           4   2               5   2
2   3          3     3            4       3
  1             2   4             3       4
                  1                 2   5
                                      1 

Rotating the code to another starting point will not change the selection of toss values or their order of occurrence.

There are two conventions: either writing the string as the pattern would need to be started and connected,
or writing the string with the highest toss value first, which is often not the same.
The second case can make code that could not be followed to start or to connect, requiring some transition.
At JuggleWiki, the second convention is used for file names, to sort at the Category to aid selection,
with the starting order shown first at the webpage, if not the same.

There are, however, many cases (more with more balls and longer codes), of valid permutations of a code,
or "versions" which do make different patterns, such as '6420' and '4602'.
In such cases, both codes could be written by rotating, such as '6420' and '6024', or '4206' and '4602'.

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