What are some ways that a leader can show their software staff that experimentation and failure are not only acceptable, but encouraged?

A good way to encourage experimentation might be to tell stories about your own experiments, and the level of success you achieved with each one.

Notice there that I referred to level of success you achieved. Nothing is ever a failure. If your experiment did not succeed it was a learning experience.

Not every experiment will deliver the outcome you expected. If it did it would not be an experiment.

Experiments are voyages into unknown territory, they should be fun. Avoid focusing on the outcome and instead talk about the process of experimentation as a goal in itself.

Add a 'what if' question to every discussion about the software development. What if we did this? What if we didn't do that? etc.

That sort of question may initially result in hostility, you are going off the plan. But eventually developers will start to accept that they are going to be asked the question so it will be a good idea to go to the meeting having thought about the What If questions and to also be able to answer those questions in the meeting, because they have already tried it.

You can reinforce your this approach by placing posters on walls or screen savers etc with messages that support being innovative. breaking the rules and challenging the status quo.

I should copyright that idea LOL

If you need me, I will be in the studio designing posters

You must begin by understanding what the impact of failure means to the organization. If failure leads to missed deliverables, breached contracts, or failure to deliver at key events such as trade shows, then it is not an acceptable outcome.

However, experimentation requires a different mindset. Assume that failure—or lack of delivery to an end customer—is part of the plan.

For example, during the late 1990s internet boom, an entrepreneur wanted to test the idea of selling cars online. Instead of fully investing in a complex e-commerce platform, he created a simple static website, bought a car from a local dealership, and resold it online. This was not a business—it was an experiment to see if people would buy cars over the internet. They did. The goal wasn’t technological success or product delivery, but learning.

To encourage experimentation, you must make it safe to fail. The best way to do that is to define experiments so that neither success nor failure directly affects business outcomes.