If you haven’t already:
brew install ffmpeg gifsicle
Open QuickTime Player. File > New Screen Recording. Record. Trim as needed. Save as foo.mov.
First compute a good color palette:
ffmpeg -i foo.mov -vf 'scale=-1:-1:flags=lanczos,palettegen' foo-palette.png
Then make your GIF:
ffmpeg -i foo.mov -i foo-palette.png -filter_complex 'scale=-1:-1:flags=lanczos[x];[x][1:v]paletteuse' foo.gif
To drop frames, add fps=10,
to the -filter_complex
argument.
To crop, add crop=width:height:x:y,
to the -filter_complex
argument.
I really like the 5€ GIFBrewery tool for creating a gif from a movie file, because it has a bunch of handy functions build in, such as captions and conversion properties. I'm sure you can do all this with free tools, but this one is designed well and works.