"DisplayDurations"
works fine but there are limits to the values it accepts, and there are also limits on the performance of the software you use to open the file.
IE
I think the main problem is with the browser not allowing such frame rates . Reportedly IE allows only a Maximum Frame-rate ~16 fps. Microsoft claims it's because Legacy compatibility.
But QuickTime Player reports that that GIF file is 100 fps, so something else must be considered.

Limited values for "DisplayDurations"
By inspection (after @Karsten), and based in the format specifications "DisplayDurations"
can have values from 1 to 65535 hundredth of a second. Therefore, given values are Mod
to 2^16 - 1
and Round
to multiples of 1/100
seconds. Zeros are interpreted as infinity (∞
).
Maximum specified frame rate would be 100 fps, but some software may chose to slow that down. Maximum delay, is 655.35
seconds.
There are very few integer number frame rates available, {100, 50, 25, 20, 10, 5, 4, 2, 1}
, and the first four are not accepted by IE.
Solution
So, considering the deplorable limitations of IE, you should lower the delay to 0.06
. Change your code to
eccentricity =
Table[Graphics[{Disk[{0.1 Cos[θ], 0.1 Sin[θ]}, 1], White, Point[{0, 0}]},
PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}], {θ, 0, 2 π (1 - 1/16), 2 π/16}];
Export["eccentricity.gif", eccentricity, "DisplayDurations" -> 0.06];
Documentation
It seems to me that the documentation in this case is deficient, as there is no mention on the limits of the values accepted for many options such as "DisplayDurations"
. So I have submitted a suggestion to the Wolfram Technical Support [CASE:3916297]. If relevant, I will update this answer with the reply, when it happens.
"DisplayDurations"
of the gif created byExport
usingImport["eccentricity.gif", "DisplayDurations"]
. The shortest possible seems to be"DisplayDurations" -> 1/100
. $\endgroup$