Termux. A Debian-based Linux system running on top of unrooted Android.
It lets you interface with your phone's functions (GPS, calls, etc.), and install packages to extend functionality.
Turned my phone into a mobile network troubeshooting device, lets me grep through my sms, and I can ssh into my server on the go.
With AnLinux you can install a full standard linux system in it, including a GUI, and connect to it with a VNC viewer. (AnLinux is just a helper script linking to some dude's repo, so if you are at all security-minded, you can also bootstrap and install any Linux distro manually).
So you could have a Debian with Gnome desktop running on your unrooted phone.