The most important property of fractals is Self-Similarity.
This means that if you zoom into any part of a fractal, it looks similar to the whole shape; no matter how much you zoom.
This “infinite complexity in a finite space” is what makes fractals so fascinating.
I certainly grant that you can imagine that the world is eternal. However, since you assume only a succession of states, & since no reason for the world can be found in any one of them ... it is obvious that the reason must be found elsewhere. ~Leibniz
Gödel's incompleteness theorem is one of those things that math popularisers always talk about as a hugely important result.
But according to @3blue1brown, it almost never comes up in practice. It's a weird pathology that nobody expects to matter for the big questions.
“What we become depends on what we read after all of the professors have finished with us. The greatest university of all is a collection of books.”
― Thomas Carlyle, On Heroes, Hero Worship and the Heroic in History