Tom Knight:
My favorite speculation for structure at the Planck scale is a 4-D crystal with dislocations in the crystal structure giving rise to observable particles. Past is represented with a solidified structure, present is the phase boundary, and quantum weirdness and interference is the attempt to extend the phase boundary in a consistent way. We observe the net growth of the crystal, but it is an epiphenomenon -- a result of the crystal growth.
:) In the late 1980s, I used an HP75C to obsessively print out evolutions of one-dimensional cellular automaton rule #193. Abstracting some of the behaviors, I wrote a short, unpublished article wherein I likened some of the cyclical behaviors arising out of this rule to cracks in a crystal composed of (a very specific pattern of) staggered size-3 'triangles' that evolve naturally out of random startups under the rule. Each crack had a positive integer associated with it that was the offset of the two crystal regimes between which it was caught. When two cracks collided, they naturally preserved the sum (modulus the crystal 'length') of their offsets. I spent some time just trying to chart the elementary cracks/particles. To me, the implication was that the stuff we now consider the real part of our Universe (i.e., elementary particles) might also be defects in some small-dimensional sea of periodic structure.