Euclidean Rhythms

1 beat
-
0
1

2 beats
---
0 0
1 0
1 1

3 beats
-----
0 0 0
1 0 0
1 0 1
1 1 1

4 beats
-------
0 0 0 0
1 0 0 0
1 0 1 0
1 0 1 1
1 1 1 1

5 beats
---------
0 0 0 0 0
1 0 0 0 0
1 0 1 0 0
1 0 1 0 1
1 0 1 1 1
1 1 1 1 1

6 beats
-----------
0 0 0 0 0 0
1 0 0 0 0 0
1 0 0 1 0 0
1 0 1 0 1 0
1 0 1 1 0 1
1 0 1 1 1 1
1 1 1 1 1 1

7 beats
-------------
0 0 0 0 0 0 0
1 0 0 0 0 0 0
1 0 0 1 0 0 0
1 0 1 0 1 0 0
1 0 1 0 1 0 1
1 0 1 1 0 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 1

8 beats
---------------
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0
1 0 0 1 0 0 1 0
1 0 1 0 1 0 1 0
1 0 1 1 0 1 1 0
1 0 1 1 1 0 1 1
1 0 1 1 1 1 1 1
1 1 1 1 1 1 1 1

References

The Euclidean Algorithm Generates Traditional Musical Rhythms - Godfried Toussaint (PDF)
Euclidean Algorithm, ユークリッドの互除法 (Wikipedia)