Last modified Tuesday, January 11, 2000 5:04 pm

Hofstadter's chaotic sequence.

1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,16,14,14,16,16,16,16,20,17,17,20,
21,19,20,22,21,22,23,23,24,24,24,24,24,32,24,25,30,28,26,30,30,28,32,30,32,32,32,32,40,
33,31,38,35,33,39,40,37,38,40,39,40,39,42,40,41,43,44,43,43,46,44,45,47,47,46,48,48,48,
48,48,48,64,41,52,54,56,...

s=4:
no period detected 1,1,2,3,3,4,1,1,2,2,2,4,4,4,2,1,2,3,3,4,4,4,4,4,2,2,4,4,4,4,4,1,1,4,1,3,4,2,1,2,3,3,4,4, 4,4,4,4,4,1,2,4,2,2,2,4,4,2,4,4,4,4,4,1,3,2,3,1,3,4,1,2,4,3,4,3,2,4,1,3,4,3,3,2,4,1,3,3, 2,4,4,4,4,4,4,4,1,4,2,4,...



shaft utilization:

    1:  16%  ++++++++++++++++
    2:  21%  +++++++++++++++++++++
    3:  17%  +++++++++++++++++
    4:  46%  ++++++++++++++++++++++++++++++++++++++++++++++

s=5:
no period detected 1,1,2,3,3,4,5,5,1,1,1,3,3,3,5,4,5,1,1,2,2,2,2,1,4,4,1,1,1,1,5,2,2,5,1,4,5,2,1,2,3,3,4,4, 4,4,4,2,4,5,5,3,1,5,5,3,2,5,2,2,2,2,5,3,1,3,5,3,4,5,2,3,5,4,5,4,2,5,1,3,4,3,3,1,4,5,2,2, 1,3,3,3,3,3,3,4,1,2,4,1,...



shaft utilization:

    1:  21%  +++++++++++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  22%  ++++++++++++++++++++++
    4:  18%  ++++++++++++++++++
    5:  19%  +++++++++++++++++++

s=6:
no period detected 1,1,2,3,3,4,5,5,6,6,6,2,2,2,4,3,4,5,5,6,6,6,6,4,2,2,4,4,4,4,2,5,5,2,3,1,2,4,3,4,5,5,6,6, 6,6,6,2,6,1,6,4,2,6,6,4,2,6,2,2,2,2,4,3,1,2,5,3,3,4,1,2,4,3,4,3,6,4,5,1,2,1,1,4,2,3,5,5, 4,6,6,6,6,6,6,4,5,4,6,2,...



shaft utilization:

    1:   9%  +++++++++
    2:  21%  +++++++++++++++++++++
    3:  11%  +++++++++++
    4:  21%  +++++++++++++++++++++
    5:  13%  +++++++++++++
    6:  25%  +++++++++++++++++++++++++

s=7:
no period detected 1,1,2,3,3,4,5,5,6,6,6,1,1,1,3,2,3,4,4,5,5,5,5,2,7,7,2,2,2,2,6,3,3,6,7,5,6,1,7,1,2,2,3,3, 3,3,3,4,3,4,2,7,5,2,2,7,4,2,4,4,4,4,5,5,3,3,7,5,4,5,2,3,5,4,5,4,7,5,6,1,2,1,1,4,2,3,5,5, 4,6,6,6,6,6,6,1,6,3,5,7,...



shaft utilization:

    1:  11%  +++++++++++
    2:  16%  ++++++++++++++++
    3:  17%  +++++++++++++++++
    4:  15%  +++++++++++++++
    5:  18%  ++++++++++++++++++
    6:  14%  ++++++++++++++
    7:   9%  +++++++++

s=8:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,2,1,2,3,3,4,4,4,4,8,6,6,8,8,8,8,4,1,1,4,5,3,4,6,5,6,7,7,8,8, 8,8,8,8,8,1,6,4,2,6,6,4,8,6,8,8,8,8,8,1,7,6,3,1,7,8,5,6,8,7,8,7,2,8,1,3,4,3,3,6,4,5,7,7, 6,8,8,8,8,8,8,8,1,4,6,8,...



shaft utilization:

    1:  10%  ++++++++++
    2:   5%  +++++
    3:   9%  +++++++++
    4:  13%  +++++++++++++
    5:   6%  ++++++
    6:  16%  ++++++++++++++++
    7:   8%  ++++++++
    8:  33%  +++++++++++++++++++++++++++++++++

s=9:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,1,9,1,2,2,3,3,3,3,7,5,5,7,7,7,7,2,8,8,2,3,1,2,4,3,4,5,5,6,6, 6,6,6,5,6,7,3,1,8,3,3,1,5,3,5,5,5,5,4,6,4,2,8,6,3,4,1,2,4,3,4,3,6,4,5,7,8,7,7,1,8,9,2,2, 1,3,3,3,3,3,3,1,5,7,9,2,...



shaft utilization:

    1:  11%  +++++++++++
    2:  11%  +++++++++++
    3:  21%  +++++++++++++++++++++
    4:   9%  +++++++++
    5:  14%  ++++++++++++++
    6:  12%  ++++++++++++
    7:  10%  ++++++++++
    8:   9%  +++++++++
    9:   3%  +++

s=10:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,1,1,2,2,2,2,6,4,4,6,6,6,6,10,7,7,10,1,9,10,2,1,2,3,3, 4,4,4,4,4,2,4,5,10,8,6,10,10,8,2,10,2,2,2,2,10,3,1,8,5,3,9,10,7,8,10,9,10,9,2,10,1,3,4,3, 3,6,4,5,7,7,6,8,8,8,8,8,8,4,1,2,4,6,...



shaft utilization:

    1:   9%  +++++++++
    2:  15%  +++++++++++++++
    3:   9%  +++++++++
    4:  13%  +++++++++++++
    5:   5%  +++++
    6:  12%  ++++++++++++
    7:   5%  +++++
    8:  13%  +++++++++++++
    9:   5%  +++++
   10:  14%  ++++++++++++++

s=11:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,1,1,1,1,5,3,3,5,5,5,5,9,6,6,9,10,8,9,11,10,11, 1,1,2,2,2,2,2,10,2,3,8,6,4,8,8,6,10,8,10,10,10,10,7,11,9,5,2,11,6,7,4,5,7,6,7,6,9,7,8,10, 11,10,10,2,11,1,3,3,2,4,4,4,4,4,4,9,8,8,10,1,...



shaft utilization:

    1:  10%  ++++++++++
    2:  10%  ++++++++++
    3:   7%  +++++++
    4:   9%  +++++++++
    5:   9%  +++++++++
    6:  10%  ++++++++++
    7:   5%  +++++
    8:  11%  +++++++++++
    9:   7%  +++++++
   10:  14%  ++++++++++++++
   11:   8%  ++++++++

s=12:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,4,2,2,4,4,4,4,8,5,5,8,9,7,8,10,9, 10,11,11,12,12,12,12,12,8,12,1,6,4,2,6,6,4,8,6,8,8,8,8,4,9,7,2,11,9,3,4,1,2,4,3,4,3,6,4, 5,7,8,7,7,10,8,9,11,11,10,12,12,12,12,12,12,4,5,4,6,8,...



shaft utilization:

    1:   4%  ++++
    2:   6%  ++++++
    3:   5%  +++++
    4:  15%  +++++++++++++++
    5:   6%  ++++++
    6:   9%  +++++++++
    7:   5%  +++++
    8:  15%  +++++++++++++++
    9:   6%  ++++++
   10:   6%  ++++++
   11:   7%  +++++++
   12:  16%  ++++++++++++++++

s=13:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,3,1,1,3,3,3,3,7,4,4,7,8,6,7,9,8,9, 10,10,11,11,11,11,11,6,11,12,4,2,13,4,4,2,6,4,6,6,6,6,1,7,5,12,9,7,13,1,11,12,1,13,1,13, 3,1,2,4,5,4,4,7,5,6,8,8,7,9,9,9,9,9,9,12,2,13,2,4,...



shaft utilization:

    1:   9%  +++++++++
    2:   6%  ++++++
    3:   8%  ++++++++
    4:  11%  +++++++++++
    5:   5%  +++++
    6:  11%  +++++++++++
    7:   7%  +++++++
    8:   7%  +++++++
    9:  10%  ++++++++++
   10:   4%  ++++
   11:   9%  +++++++++
   12:   8%  ++++++++
   13:   5%  +++++

s=14:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,2,14,14,2,2,2,2,6,3,3,6,7,5,6,8,7, 8,9,9,10,10,10,10,10,4,10,11,2,14,12,2,2,14,4,2,4,4,4,4,12,5,3,10,7,5,11,12,9,10,12,11, 12,11,14,12,13,1,2,1,1,4,2,3,5,5,4,6,6,6,6,6,6,8,13,10,12,14,...



shaft utilization:

    1:   5%  +++++
    2:  12%  ++++++++++++
    3:   6%  ++++++
    4:   9%  +++++++++
    5:   7%  +++++++
    6:  12%  ++++++++++++
    7:   3%  +++
    8:   6%  ++++++
    9:   4%  ++++
   10:  11%  +++++++++++
   11:   6%  ++++++
   12:  11%  +++++++++++
   13:   2%  ++
   14:   6%  ++++++

s=15:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,1,14,14,1,1,1,1,5,2,2,5,6,4,5,7,6, 7,8,8,9,9,9,9,9,2,9,10,15,13,11,15,15,13,2,15,2,2,2,2,10,3,1,8,5,3,9,10,7,8,10,9,10,9,12, 10,11,13,14,13,13,1,14,15,2,2,1,3,3,3,3,3,3,4,11,7,9,11,...



shaft utilization:

    1:  10%  ++++++++++
    2:  11%  +++++++++++
    3:  10%  ++++++++++
    4:   3%  +++
    5:   6%  ++++++
    6:   5%  +++++
    7:   4%  ++++
    8:   7%  +++++++
    9:  11%  +++++++++++
   10:   8%  ++++++++
   11:   6%  ++++++
   12:   5%  +++++
   13:   5%  +++++
   14:   4%  ++++
   15:   5%  +++++

s=16:
no period detected 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,16,14,14,16,16,16,16,4,1,1,4,5,3,4, 6,5,6,7,7,8,8,8,8,8,16,8,9,14,12,10,14,14,12,16,14,16,16,16,16,8,1,15,6,3,1,7,8,5,6,8,7, 8,7,10,8,9,11,12,11,11,14,12,13,15,15,14,16,16,16,16,16,16,16,9,4,6,8,...



shaft utilization:

    1:   6%  ++++++
    2:   1%  +
    3:   4%  ++++
    4:   5%  +++++
    5:   5%  +++++
    6:   8%  ++++++++
    7:   5%  +++++
    8:  15%  +++++++++++++++
    9:   4%  ++++
   10:   4%  ++++
   11:   5%  +++++
   12:   8%  ++++++++
   13:   1%  +
   14:   8%  ++++++++
   15:   3%  +++
   16:  18%  ++++++++++++++++++

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e-mail: ralph@cs.arizona.edu

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