The de Bruijn Torus
The de Bruijn Torus
In the de Bruijn sequence , all items of order two from the alphabet of size four are cyclically represented. Those items are , , , and so on.
0010203112132233
{0,1,2,3}
00
01
10
02
In the de Bruijn sequence , all order-four items from the size-two alphabet are cyclically represented. In this case, the items are , , and so on.
0000100110101111
{0,1}
0000
0001
0010
In general, the order- de Bruijn sequence for a size- alphabet has length . There are different sequences.
n
k
B(k,n)
n
k
n-1
k
(k!)
n
k
B(k,n)
For a de Bruijn torus, all -matrices from a size- alphabet have toroidal representation in an array.
(m,n)
k
In this Demonstration, de Bruijn tori for ternary , quaternary , binary and binary are shown. Choose an index number with a slider; the de Bruijn torus is rotated to place the corresponding matrix in the upper-left corner of the array.
2×2
2×2
3×2
3×3
External Links
External Links
Permanent Citation
Permanent Citation
Ed Pegg Jr
"The de Bruijn Torus"
http://demonstrations.wolfram.com/TheDeBruijnTorus/
Wolfram Demonstrations Project
Published: January 1, 1999