“I can see how experimenting and letting go of the outcome can increase the joy of painting but how does that square with the desire to improve continually and do your best work? Does one just have to trust that experimenting will lead to better results in time? ” — Eddie
My short answer is “yes”.
My longer answer starts with seeing the journey as circuitous and tangential not linear, much as it would be easier if it were.
Being open to trying new things, materials, subjects, approaches simply to see what happens, to see where it may lead you. Taking the bits you find interesting and intriguing further on the journey (not necessarily the same as the bits you like or others regard as successful) whilst shrugging off what turned out to be hideous, discarding that which was unenjoyable. Always remembering, some things may be a matter of wrong place, wrong time; it’s not necessarily a never again situation. Then mixing the new with the existing, the familiar and the favourites.

Happy accidents become familiar by deliberately trying to repeat the result. Even with not entirely controllable techniques predictability increases with repetition as you acquire knowledge of the range of possible results, and how you might respond to these.
Spending time looking at what you’ve done, pinpointing what you like and don’t, what you might try again and won’t, is part of the journey. Don’t throw things out too soon, in the emotion of the moment. Do it dispassionately at a later date.
It should be like pure science, research to see what happens and to learn, driven by curiosty, rather than applied science, driven by a desired outcome. Intertwined but with different approaches, hopes and expectations, for different times and projects.
Paint, play, ponder, paint, that’s my path.
In an interview I read earlier today, author Susan Steinberg describes her writing process in a way that I think fits painting and drawing too, of it emerging not coming out fully formed first time:
“There are several writers who have told me that they assume that when I sit down to write, that I write a sentence and then I don’t move on until that sentence is perfect. And then I write the next sentence and that’s how I write. And when they find out that that I make the biggest mess you can imagine. I just write and write and it doesn’t always make sense and I go really far out there and then pull back and start to pare it down.”
(source: Susan Steinberg on the Value of Writing an Ugly Draft by Diane Cook, Literary Hub, 23 August 2019)
Excellent thoughts — and excellent illustrative graphic!
A very thoughtful and thought-provoking answer. I love the Venn diagram which I could ponder for ages.