What a wonderful post this is! I first encountered Julia fractals while taking a masters class in chaos theory, technically a physics class. It was a masters of liberal arts program so you got a little bit of everything... I hadn't taken math since high school, really, and the class utterly annihilated my conception of the world.
I remember the Julia fractal in particular because it was so beautiful, and it was around this part of the course -- maybe 75% of the way through -- that the fractals and like topics started to blow my mind. Our professor showed us this video that zoomed in on a Julia fractal, something like this, https://www.youtube.com/watch?v=gruJ0S3TTtI, and I remember watching it all day at work the next day. I also searched for images of the most beautiful Julias to make as my desktop background, of course.
Not only were they beautiful but so symbolic, as this article captures: Julia fractals are part of chaos theory, which holds that even determinate, logical systems can nevertheless manifest completely unpredictable and nonrecurrent behavior. It's a straightforward equation that gets you these beautiful -- and utterly terrifying, ceaseless, dreamlike -- images, when mapped in a certain way. For me, that's a really beautiful concept because with "Enlightenment" mathematics, Newton and Leibniz and co, you got this concept of a determinate universe, which could therefore also be known and predicated in advance. Yet chaos theory shows that even determinate systems can be impossible to know, refusing to allow the complexity and variety of that which exists to boil down into a boring pattern of predictable and even controllable outcomes.
I remember the Julia fractal in particular because it was so beautiful, and it was around this part of the course -- maybe 75% of the way through -- that the fractals and like topics started to blow my mind. Our professor showed us this video that zoomed in on a Julia fractal, something like this, https://www.youtube.com/watch?v=gruJ0S3TTtI, and I remember watching it all day at work the next day. I also searched for images of the most beautiful Julias to make as my desktop background, of course.
Not only were they beautiful but so symbolic, as this article captures: Julia fractals are part of chaos theory, which holds that even determinate, logical systems can nevertheless manifest completely unpredictable and nonrecurrent behavior. It's a straightforward equation that gets you these beautiful -- and utterly terrifying, ceaseless, dreamlike -- images, when mapped in a certain way. For me, that's a really beautiful concept because with "Enlightenment" mathematics, Newton and Leibniz and co, you got this concept of a determinate universe, which could therefore also be known and predicated in advance. Yet chaos theory shows that even determinate systems can be impossible to know, refusing to allow the complexity and variety of that which exists to boil down into a boring pattern of predictable and even controllable outcomes.