To run this with "Heirloom Development Tools" m4, or similar legacy m4, you likely have to increase the stack size. "m4 -S 1000 mandel.m4" works for me with Heirloom m4. Also tested with GNU m4 and OpenBSD m4, but written to require no more than the ASCII character set and the POSIX standard for m4.

There are no global variables, except that I do not bother with pushdef-popdef for the few temporary variables. The stack is numbers separated by ‘:’. Variables are stored in a manner similar to a Common Lisp plist and so are referenced by name: ‘var0:123:var1:456:var2:789:’

I do not play those terribly confusing tricks with commas, as so much m4 code does. This is more like programming in Prolog or a term-rewriting language (such as Pure), I guess.