It might be the limited capabilities of the gif file format, like it only supports a maximum of 256 colors (8-bit), while the filter makes use of 24 bit colors.
One way to capture it better might be to use something like OBS (Open Broadcaster Software) to capture it like a video. But then you will have compression artefacts, which may or may not invalidate the effect you want to capture.
I don't really know of any way to capture a video which fully do justice to the filter. It really is best viewed live.