Whenever I would see Mandelbrot zoom videos pop up on my YouTube, I would always watch the entire thing. It always amazed me.
Recently I thought how "much" are we zooming in. How small of a point in the complex plain are we going. Each video gives a number for how far they are going, but that doesn't mean anything. I figured I could go and scale the set as if it were a real world object being zoomed in on, then I could get a better grasp by how small we are going.
I decided I would scale the area of The Mandelbrot Set to the area of the universe. Assuming they are both flat of course.
For the Sets area I used what is called the Escape Radius, which typically is 2.0 on the complex plain. A = 4.0pi
And for the universe I used a rough estimate of its diameter being 7trillion light years. U = upi (too many numbers to type out, the calculations don't matter tbh for my question)
The number that represents how far was zoomed I used Z.
The equation I got was
upi/x = 4.0pi/Z upi*Z = x*4.0pi (upi*Z)/4.0pi = x uZ/4.0 = x (canceled pi)
So I have x equal to the zoom on the universe, but the issue I have is I am lacking a unit. Assuming my math/understanding of The Mandelbrot Set (if it is please let me know) isn't flawed, then all I need to put this into proportion is a unit for x. Basically, if I am looking at the entire universe at once, and I pick a random point in the universe, and I zoom there by x, what is the x's unit? This is probably super simple and I'm just missing it.
Sorry if tag is off