Inspired by this Gist and @coryodaniel's solution,
I put the script inside a babashka script, called pdf-like-fax.clj
:
#!/usr/bin/env bb
(defn pdf-like-fax [input output]
(let [sign (rand-nth ["+" "-"])
rotation (rand-int 1000)
cmd (format "convert -density 150 %s -rotate %s0.%s -attenuate 0.4 +noise Multiplicative -attenuate 0.03 +noise Multiplicative -sharpen 0x1.0 -colorspace Gray %s" input sign rotation output)
prepared-cmd (str/split cmd #" ")]