The type of fractal art I make relies on an iterative rendering process. The current state of the render is fed back in to the same algorithm as an input to find the next state, and this repeats millions of times to produce the pretty images I share with you. It's amazing to me the complex shape of a fractal can be found by repeatedly iterating a simple set of mathematical rules. There is some underlying mathematical truth, and this iterative process loops on itself to get closer and closer to rendering it.
My fractal workflow is highly iterative too. I'm usually not setting out with a goal in mind, I'm looking at what's there and imagining how to make it better. My designs change quite wildly on their way to a finished render, and I have to caution anyone looking over my shoulder not to get too attached to what they see because it likely won't remain.
Iterative processes are found all over, not just in niche recreational mathematics. Driving a car, for example, uses an iterating strategy. You may plot your route out before you start, but you don't plan every physical motion you'll make as some kind of dance routine. That wouldn't work, because you can't predict everything about traffic and the state of the road perfectly.
Instead, you use a strategy that allows you to react to the current state of the road around you. The strategy needs to be able to shift when there are other cars near you, or stop lights, or other traffic control signs. It needs to be resilient if the intended route is blocked for some reason. If you're wise, your strategy also includes a way to react to everything going wrong, like calling for help.
But what happens when you encounter a new sign, one clearly meant to direct the way you operate your car, but using symbols you've never seen before? Perhaps you'd continue driving, watching other drivers to see if they make any changes. Maybe you'd pull over and look up what the sign means. But what you probably wouldn't do is decide you're a terrible driver and give up driving forever, right?
You know from experience that part of being a driver is being able to navigate new situations with your vehicle, you did a lot of that when you first started driving. You know that with a little bit of learning and a little bit of effort, you can adjust your driving strategy to fit this new situation. You take your current strategy as the input, change it with the new information, and arrive at the next iteration of it.
I often encounter artists who are held back by their fear of failure. In a competitive perspective, anything short of success is loss. If I do something poorly, I'm worse off than when I started. But in an iterative perspective, failure is a normal and expected part of the process, it would be weird if I didn't fail a bit. My portfolio might only show my best works, but my archives are full of bad art that helps me remember what doesn't work. Both played important roles in my growth.
The fear of making "bad" art hurts an artist in two ways. It convinces them not to try, and then, when they do try, it creates an intense pressure not to fail. This can quickly spiral into a self-reinforcing feeling of being "not good enough". In a twisted way, this fear is a way of punishing the artist for the potential of making bad art. It's accepting the worst outcome to avoid a bad outcome.
An artist who instead decides that they can learn from their failures has less reason not to try. If every attempt is seen as a step forward, you don't have to worry about whether you're going in the right direction, you can focus on the pace and the length of your strides. Even better, each new piece gives you a fresh opportunity to re-examine your strengths and refine your focus. To iterate your own artistic skill. The more often you do that, the more confident you'll be in your ability to make art, because the end result won't feel so mysterious and scary.
I've been thinking about this perspective a lot, for well over a year now, and it resonates in a way that feels not just truthful, but natural. I can apply an iterative perspective to almost any situation, and it's really changing my focus in a lot of things. I'm finding it much more rewarding to experiment and explore, and I'm spending a lot less time fixated on the ways I might fall short of some idealistic state. It lets me let go of ideas that are no longer helpful, even if they used to be important to me, without feeling like anything was wasted or lost. It even helps me engage with people, instead of letting a disagreeable aspect turn into a wall between us.
There's lots that could be said about how iterationist perspectives apply to various aspects of life, enough that it could probably be fleshed out as a philosophy. But one thing I appreciate about this kind of thinking is that it doesn't descend from an external truth. It's not founded in a fundamental idea of "right", it's just a way to model progress. My views on iterationism are themselves subject to iteration, of course, but as those iterations reveal new problems it's just an invitation to devise something more useful. It turns out, just like a fractal, the closer I look for truth, the more detail I find.