sorry to say but no max for arduino (ATMEL), ARM, PIC or LINUX etc.
smallest computer you can run max on would be a micro form factor pc (WINDOWS) or macmini (OSX)
i had success with fit-pc > http://www.fit-pc.com (1/4 size of macmini, between 200-1000$ based on spec).
note there could be smaller/cheaper pc flatforms, search for "windows computer-on-module "
but beware, some of the more exotic CPUs (not AMD or intel) used on those tiny pcs will not be able to pass max authorization, better check with iLok people before you buy anything weird.
Take a look at Raspberry Pi.
It is not a microcontroller, it is a very small single board computer that boots Linux.
It is roughly the same size as an Arduino board.
It has 8 GPIO lines in case you need them.
The downside is that it only has 256MB of ram. After booting a minimal linux distro, there’s not much left for applications.
I would be surprised if something as big as Max would run in < 256MB, but it's worth a try.