How about some sort of Euclidean generator and something similar to the Turing machine.
Agra that would be awesome stuff to have
If I would ask you to explain the benefit of such a feature to me, in simple words, how would you do that?
Euclidean algo is great for “exotic” rhythms. Combining several of these can make pretty complicated poly rhythm style music. Like rhythm found in African style music among a lot of other exotic rhythm styles.
What it basically does is distribute the amount of wanted hits as evenly as possible according to the length you want.
So if you for example say you want 4 hits on a 16 step sequencer it would be:
X 2 3 4 X 6 7 8 X 10 11 12 X 14 15 16
(X are the 4 hits that will be played back)
That’s pretty simple, cause 16 can be divided by 4, so they steps will be distributed as 1/4 notes.
Another more exotic example, if you want 6 hits on a 13 step sequence:
X 2 3 X 5 X 7 X 9 X 11 X 13
(X are the 6 hits that will be played back)
This is a bit more exotic rhythm.
Anyway, I hope you get the idea 
There are lots of papers, explanations on Youtube on the web if you want to dig more into it.
For example:
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It’s really simple to make in Pure Data. Google a bit, there are many patches, IIRC also a turing machine style euclidean sequencer.
Turing machine shifts bits left and then runs them through a DAC, randomly flipping the least significant bit.
It might be fractal, but it’s not euclidean.
I know, but that’s what many people call these types of sequencers.
My point was not really about what was the correct term, my point was that someone already made it for PD 
the LXR-02 has a great implementation of the euclidean algorithm. just three values: length (the number of steps in the pattern), step (the number of steps to be distributed as equally as possible within the pattern), and rotate (where you can move the resulting pattern forward or backward a step in time). it’s very valuable for creating beats: almost all standard rhythms are variations of the algorithm-- after generation you then add or subtract beats to taste, of course. it might be a great set of extra options on the arpeggiator?
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A euclidean generator would still be great to have 