You can clone with
HTTPS or Subversion.
No mattter if I resize my browser or use a mobile user agent, the ai-cache folder remains empty.
I don't know how to actually debug adaptibe-images.php.
How should I know if the script works at all?
OK, the firs thing to check is that your .htaccess is working correctly. Make sure you've got a test.jpg file in the same folder that your .htaccess file is. Open up the .htaccess file and replace
RewriteRule .(?:jpe?g|gif|png)$ adaptive-images.php
RewriteRule .(?:jpe?g|gif|png)$ test.jpg
If your htaccess is working then every single image on your site will become the test.jpg image. If not, then there's something wrong with your htaccess file or Apache configuration.
Assuming that it works, change it back and then go into the PHP. At the top of the PHP file (but inside the PHP tags) write the line:
sendErrorImage("there is a problem");
Reload your page - all images should now be replaced with a black image that contains the error message "there is a problem". If that doesn't happen, then either you've not got the files in the right place and so the htaccess file is pointing at a non-existent file, or PHP isn't working properly.
If that did work and you got a black error image, then it's a case of using that to debug your server and find out where in the code things are breaking.