I've gotten them to be creative in ways that were unexpected, like outputting tokens that have absolutely no (obvious) relation to the current conversation
While trying to iterate on a name for a product, I had it output an internal monologue alongside outputting name ideas.
With each iteration of naming I'd ask it to probe its understanding in of human creativity and list how the usefulness/realism of the internal monologue.
After a few loops the internal monologue started modeling fleeting memories about things like "that time at camp where X happened".
Eventually it was modeling fleeting thoughts like "the warmth of the cup of coffee on the desk" as a source of inspiration, and random observations like "it looks like traffic is picking up outside, getting to yoga will take a while" in the middle of a name generation task
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I made a website predicated on a similar idea after that: https://notionsmith.ai
Technically it's a hallucination generator, but I think you described why I made it (creativity and hallucinations really are similar for both LLMs and humans)