Experiments you can run yourself.
As we zoom into the boundary of the Mandelbrot set, we keep seeing new, similar structures.
After infinitely many iterations the length of the Koch snowflake is infinite, yet its area is finite.
The area of the Sierpiński triangle tends to zero after infinitely many steps.
In the chaotic regime a tiny change in the initial conditions leads to a completely different result.
A one-dimensional continuous line can fill an entire two-dimensional square.
After infinitely removing the middle thirds, what remains is a set of length 0 that is nonetheless uncountable.