A fractal is a form of iteration as I think of it, in where some outcome is used to iterate the next step? And it's fairly simple to construct one but it gets very complicated, very fast, as it evolves. But the thing is that there should be some way to back track it if it was so? Track the 'x' backwards so to speak. What would that x be here? You can't call it a constant as it is more of a relation to the equation, but if it was so then we probably would have to take a new look at 'constants' as they too should change if the universe was fractal?

Or can you have constants existing in a fractal?

I'm not sure at all there.

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The other side are those constants, similar to the Feigenbaum constant, in where you find yourself unable to back track a evolving pattern as the bifurcations (splits) are unpredictable, although still finding a constant describing the pattern.

That one might be plausible for our universe too, maybe

But they are like two sides of a coin to me.

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To make the universe into a fractal you would need it to explain how light always can have the same 'speed' when measured, not caring about your own 'relative' motion, or what direction in where you measure it. Find a way to describe a fractal having that property and I would be very interested.