I am trying to resize an image (using imagemagick) to keep it's current aspect ratio but fit it into a 4/3 container.
This is the command I have so far:
magick convert ./horse.jpeg -background white -gravity center -extent 4/3 ./hourse_output.jpeg
This is what I'd like: 
. As you can see, the image is "put into" a 4/3 container.
My error. The aspect ratios such as 4:3 in ImageMagick -extent will only crop and not pad.
See my bash unix script "aspectpad" at http://www.fmwconcepts.com/imagemagick/index.html, which does what you want I think.
Nevertheless, here is a partial solution for how to do it. But this only works for landscape mode input. Also only with ImageMagick 7 due to the use of inline arguments for -extent. You would have to modify it for portrait mode.
Input (aspect 2:1 = 2/1 = 2):
magick barn_2to1.jpg -set option:wd "%[fx:(4/3)>(w/h)?(4/3*h):w]" -set option:ht "%[fx:(4/3)>(w/h)?h:(w/(4/3))]" -gravity center -background black -extent "%[wd]x%[ht]" result.jpg
Output (aspect 4:3 = 4/3 = 1.33):
Note, that I used background of black so that it was visible here. Change to any other color you want.
If the input landscape aspect is larger than 4:3 (4/3), it will pad on top/bottom. If the input landscape aspect is smaller than 4:3, it will pad on left/right.
Input (aspect=1:1 = 1/1 = 1):
magick lena.jpg -set option:wd "%[fx:(4/3)>(w/h)?(4/3*h):w]" -set option:ht "%[fx:(4/3)>(w/h)?h:(w/(4/3))]" -gravity center -background black -extent "%[wd]x%[ht]" result2.jpg
Use 4:3 not 4/3. But you have not specified any -resize. In ImageMagick 7, use magick only, not magick convert and not convert. For other tools, use magick identify, magick mogrify, etc. But not for convert. See imagemagick.org/script/command-line-processing.php#geometry for the 4:3 issue.
Here is one other way to do it in ImageMagick, if you know the picture is in landscape mode and the image w/h aspect is larger then 4/3. Just pad the top and bottom with plenty of room and then use -extent 4:3 to crop it. This way no computations are needed, so it should work in ImageMagick 6 or 7. If ImageMagick 6, change magick to convert. (If the w/h is less than 4/3 landscape, then pad the left and right.)
Input:
magick barn_2to1.jpg -gravity center -bordercolor black -border 0x100 -background black -extent 4:3 result3.jpg
