The nature of fractals and how we visualised Mandelbrot gives the impression of infinity, but if you look, it is a constant repetition of the same process and is not transferable to reality

It actually is transferable to reality. The repetition is call iteration and yes, it is self similar at different magnitudes but always slightly different. The fact that this mathematical concept is transferable to reality is the key aspect of it. Now we know that seemingly random processes like clouds, pine trees, forests, coastlines, heartbeats, brain signals, a head of lettuce, seashells, waves, even our conversation, and a multitude of non-linear dynamic processes, perhaps everything in the universe, contain fractal properties. This is the revelation of Chaos theory. It's not about chaos but order. An order that exists in that which we thought was chaos.

... or so I understand