I suggest you backup your system before doing this because you never know what could go wrong when. Don't want to scare anyone off it's just better to be safe rather than sorry. I've done this on 3 computers and haven't had any issues.
Step 1: Selecting Your New Splash Screen
Good searches would be: "Ubuntu splash screen", "Splash screens for ubuntu", and "Incredibly awesome amazing ubuntu splash screens that are just really awesome."
You will need the .deb package for this method and yes the link gives the .deb package.
Step 2: Installing the Splash Screen
*NOTE. If after you click install and it says that the package is of bad quality you may want to do some searching and make sure that it won't cause problems. If you're wanting the one I've supplied a link to it will say this, however it works perfectly on my computer (HP Pavilion dv6). I can't garuntee that for all, but it is compatible with 13.10
Step 3: Terminal Time!
sudo update-alternatives --config default.plymouth
After pressing enter it will show a few options. Just find the one you want by reading the last bit of the middle text and type the corresponding number. In the picture I typed 2 because that was the number for Ubuntu Sunrise. Then copy and paste:
sudo update-initramfs -u
Don't close the terminal right after entering the above command! It takes a little bit of time to complete, just wait until it is finished running it. You can tell when it's finished by checking to see if says user@computer:~$