The answer probably involves ffmpeg, which is how a lot of animations are made. Packages vary as to where and how ffmpeg fits into the tool chain. VIdeoIO provides access. It might depend on how you want to create the image stack which is the input to ffmpeg.
x = 0:0.01:2*pi
anim = @animate for i in 1:200
plot(x, sin.(x .+ i / 10.0), legend = false, size = (400,200))
end every 2 ;
gif(anim,"anim.gif") # then you can also change to .mp4 or .mov
#gif(anim,"anim.mp4") # this one usually works. If not,
#then you need to check ffmpeg.
I’d forgotten I’d seen this somewhere - but I did look at the Plots docs this morning under the topic of animations, and it does not mention any other options than GIF (http://docs.juliaplots.org/latest/animations/). I’ll try this again, but I have a vague memory of having issues with the generated mp4 files (wouldn’t play on my system or something).