marcus

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## Main Question or Discussion Point

**What does "like a fractal" mean, talking smallscale spacetime**

A poster asks:

"What is meant by spacetime is a fractal, fractal like or has a kinky fractally structure ?

I know what a fractal is and what they look like, so is it an appearance of fracticality or actually fractal and does the reductablity of the pattern ever stop at a cut off volume ?

also how does one get half a spatial dimension or half a temporal dimension surely a half is still a whole when talking of dimensions?"

How do you reply? Does anyone want to take a shot at this?

Can you think of ways in which a topological space with distance function d(x,y) could be LIKE a fractal but not actually BE a fractal?

this is basically a challenge to one's intuition isn't it? How usable is your intuitive grasp of what a fractal is like?

In basic

**nonperturbative spacetime dynamics**papers Renate Loll and others are sometimes saying that the picture of spacetime emerging from their work (in CDT path integral, in Reuter renormalized quantum Gen Rel) is FRACTAL-LIKE AT SMALL SCALE. So that is the context we are talking.

"FRACTAL-LIKE" is NOT A TECHNICAL TERM so strictly mathematically speaking it does not mean a blooming thing. This is a purely intuitive notion: LIKE (in some appropriate sense) a fractal.

historically, sometimes vague intuitive notions come first and then some helpful math-minded person devises a rigorous precise technical meaning later, that you can define mathematically and that everybody agrees seems to correspond to the original vague idea. But I certainly am not at that stage and I didnt see Loll or Reuter give a definition yet. so AFAIK we are still at square one meaningwise.

Does anyone else want to take a shot at this person's question? What does LIKE A FRACTAL mean to you? I will probably take a shot at it, but am not guaranteed to be able to provide the best intuitive take.

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