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Would M-sets exist within it at specific time and/or location values?   

Also the universe (apparently) has both upper and lower boundaries i.e. size of Universe and Planck constant therefore it cannot contain any complete mathematical fractal where one or both boundaries are infinite.

  It was actually a bit of a mind provoking joke.  I've seen images of the M-set, although obviously not the full infinitely iterated set, as per David's point. 

  David's point brings up the (slightly tangential to David's point) thought that the computational capacity of the universe may be finite, which would imply that there couldn't be complete M-sets within it (if the universe's computational capacity is finite). 

  Not that I would know how to calculate the computational capacity of the universe.  I've had various ideas on it, including the possibility that it constantly increases at a linear or exponential rate, for example if the 2nd law isn't exactly correct, but there is constant 'creation of energy' as the universe expands.

  Say that spacetime has a specific wavelength (the size of the universe).  As spacetime's wavelength increases, the total wavelength of energy within the universe (the de Broglie wavelength of matter and the wavelength of photons within the universe) is a constant in relation to itself, but in relation to the universe's wavelength it constantly becomes smaller.

  Now, as the wavelength of one particle is measured versus the wavelength of another particle (which is similar to saying the energy of one particle is measured versus the energy of another), we can see that as the universe expands, the ratio of the wavelength of matter to the wavelength of the universe decreases.

  So we have a situation in which the universe (spacetime) constantly increases wavelength (decreases energy) compared to the matter within it.  Or we could say that matter constantly increases energy compared to spacetime.  Could this mean matter's computational capacity in reference to spacetime increases as long as spacetime increases wavelength?  After all, if this is true, and the M-set is a piece of spacetime rather than a piece of matter, it would seem that the capacity of matter to compute the M-set would increase indefinitely as spacetime increases. 

  Anyways, what happens when matter/energy's wavelength is many orders of magnitude less than the Planck length in comparison to the size of the universe and then it (matter/energy) runs into spacetime (when they both have specific wavelengths that achieve harmonic resonance)?

  Is spacetime imparted with all or some of the energy of matter/energy?

  Does spacetime then collapse to a much smaller size (assuming a collision in which energy is gained/lost equally spacetime would have a GREAT decrease in wavelength, or a gnaB giB)?  Or does spacetime have infinite energy which it constantly imparts upon matter/energy by "running into it" (expanding) which implies infinite computational capacity (sounds a little bit like various religions' God)?