The Best of Many Worlds
A Canticle for Leibowitz is neither a full-on science fiction story nor an entirely literary novel. It's both, existing in that extra-dimensional space between genre conventions. And so it makes sense that its writing style would enjoy a bit of extra-dimensional depth as well.
Consider this scene:
Zerchi sat on the floor in the midst of the litter and tried to massage the involuntary tremor out of his forearm, which had been recently electrified while exploring the Autoscribe's intestinal regions. The muscular twitching reminded him of the galvanic response of a severed frog's leg. (24.63)
We can see science fiction's influence on the writing style in the nonce word, Autoscribe. Science fiction writers love their nonce words—that is, words made up for a particular occasion and not the more recent uses of nonce.
We also see science fiction's influence in the "galvanic response of a severed frog's leg." Science fiction stories often craft images, similes, and metaphors around technology and scientific history, and this image is a direct reference to Luigi Galvani's famous experiments with electricity and frog legs.
(Fun fact: Galvani's experiments served as the inspiration for another famous science fiction novel, Mary Shelley's Frankenstein.)
The literary influence comes in the form of sentence structure. The sentences vary in size from short to long but tend, more often than not, to be on the longer side. Like the first sentence in the example above, they tend to be compound-complex sentences and mostly back-ended.
In other words, they connect many different clauses together, but generally start with a very simple subject and verb—in this case, "Zerchi sat." Then they provide the details in the sentence's back-end.
If you want to see an exquisite example of this sentence type in literary fiction, pick up any William Faulkner novel or short story.
Of course, A Canticle draws on a host of other traditions, not just science fiction and literary fiction. And so we wouldn't be surprised to hear someone arguing for an experimental writing style, or even a classical one.
Rather than taking our examples here as the be-all-end-all, you should simply consider them a good start. You might just find your own, personal undiscovered dimension inside of the novel. Whee.