Whenever I sit down to practice I try to give myself at least five minutes of just making noise on my instrument. I'm not really just making noise, but I'm giving myself a little bit of time in which I can experiment and try new things. I usually do this after my warm-ups and largely just let my fingers, hands, arms move freely. Sometimes a little melody will emerge and I'll play variations of it. The point of this is really twofold. First it kind of fun after having engaged in a series of warm-ups that, in and of themselves, are not very exciting. Secondly, sometimes I discover a little fragment or short melody that I wouldn't have found otherwise. When this happens I play some variations over the melody and then take a moment write it down. This fragment usually sits in my notebook unattended to for some time. I then given another look and sometimes it gets transformed into the core of an actual piece of music.
The idea of giving myself this freedom to make noise comes from William Westney's The Perfect Wrong Note. When I first read this book, I enjoyed it as a good read. I've actually gone back and read it a few times now and have become more appreciative of its central ideas. Many books on practicing (and indeed many teachers) encourage you to have a plan for your practice. While this may be useful in preparing for a performance or audition, it oftentimes doesn't let you explore your creative ideas. What I like about Westney’s book is that it encourages you to let yourself play in an undirectied and unstructured manner. The idea here is to try to find that "perfect wrong note" or "divine mistake" which brings your ideas together and gives your music or performance that spark which makes it unique.
Beyond finding a perfect wrong note in music, there are plenty of cases of technological innovation which have been the result of "finding the perfect wrong" way of doing something. For example, sticky notes were discovered by 3M after a failed attempt to make an adhesive. (Similarly, the dust masks made by 3M were the result of their failed attempt to make disposable bras.) In terms of technology, I've been told that the manner in which glasses poured to obtain a flat surface was discovered by a son of the original Pilkington of Pilkington Glass. Apparently he knocked over several mold of molten glass. When the glass cooled, it was perfectly flat. His accident (although resulting in minor injuries and damage to equipment) led to a technological improvement.