Dark Satanic Mills on a Cloudy Day is the name given by N. J. A. Sloane (OEIS A326499) to the pattern obtained by plotting the excess values of sparse rulers in batches of maximal Wichmann rulers, illustrated above.
In particular, the maximal length for a Wichmann ruler with 
segments (
marks) is 
for 
,
giving 3, 6, 9, 12, 15, 22, 29, ... (OEIS A289761)
for 
,
3, .... Prepending 0 gives block lengths from the consecutive differences 3, 3, 3,
3, 3, 7, 7, .... Writing the excesses in these blocks 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.
