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.