For anyone interested in the technical side of how Matt writes and composes on the guitar, here are a few interesting interviews he gave to guitar magazines.
The second one isn't an interview with Matt, it's really just a guitar magazine doing the detective work a guitar magazine does, it's a little generic but it's still mildly interesting. There's obviously a touch to Muse's work and Matt's instrument writing that no broad formula could ever capture, but for a bit of analysis, you might like these.
Metal guitar songwriting tips (when you've run out of ideas)
Learn how to play a riff or lick that you love. Then, tweak the hell out of that thing. Change a chord, change the sequence of notes, use a different picking technique, add or remove notes, just continue making changes until it sounds distinctly different.
Listen to an existing guitar part and then try to come up with something that has vaguely the same kind of sound/feel. Don't try to figure out the exact notes of the original guitar part, just go with the flow and if your idea kinda resembles that, you're good.
Experiment with a drum track to come up with riff ideas that suit the drums.
Take a couple of bars (for example 4) that make up a riff and experiment with changing around the order - example: playing bar 3 first, then 1, then 4. Tweak accordingly.
If you want to come up with something potentially much more wacky (tech death ninjas unite), write down a couple of intervals and/or chords you really like. Assign numbers to them i.e. 1-6. Plug into a random number generator to determine the order in which to play them.
These are my favourite methods for coming up with song ideas, especially number 1 & 2.
Note — do bear in mind while voting, iconic ≠ personal favourite, it’s more about memorability, instant recognition, cultural impact, on an objective level.
Also note — this poll is about the primary guitar riff featured in each song, more than overall song itself