Plotting the excess values of sparse rulers in batches of maximal Wichmann rulers leads to a pattern called "Dark Satanic Mills on a Cloudy Day" by N. J. A. Sloane (OEIS A289761), illustrated above.
In particular, the maximal length for a Wichmann ruler with 
marks is 
,
giving the sequence 0, 3, 6, 9, 12, 15, 22, 29, ... (OEIS A289761)
for 
,
1, .... So writing the excesses in blocks of length given by the differences of conseuctive
values 3, 3, 3, 3, 7, 7, ... gives
 |
Plotting these values when rotated 
counterclockwise gives the Dark Satanic Mills on
a Cloudy Day pattern. All the windows in the Dark Mill are Wichmann constructions.
Due to this pattern, it is believed Wichmann (1963) solved the problem. However,
of the black (
) excess values in this picture, only the leftmost six are
verified (up to length 213), while the rest show the best constructions known. It
is therefore an unsolved problem if clouds actually exist.
