The question of the sperm's motility was not meant to refute your hypothesis about dimentionality, but the graphing of the sperm due to the water flow. Surely the direction of approach is not as important as the spatial relationship between the location of the origination of the sperm and the site of the egg, even given the fact that the fertilisation takes place on a prothallus of a different individual, even though self fertilisation is not ruled out entirely. The symmetry question is entirely of the morphology of the prothallus I would have thought, not the sperm anatomy (though I can see the the symmetry of the sperm would affect its path towards the egg, though I can't see how this would be significant).
I don't think that water has a randomisation force, unless you are thinking Brownian motion effects?
Anyway, the non-determenistic nature of chaotic attractor of the complex plane certainly could be affected by a directed motion of a motile sperm towards the egg.
In a 1D symetry, or a symmetry greater than 1D, but less then 2D, (fractal dimension) the symmetry should certainly be independant of directionality of the motile sperm.
Gametic unions in the phase space of the prothallus, if they are non determenistic, should not be a precursor to the form of sexuality, even if expressed by different chromosomes IMO.
Let's hope that this communication is not lost as readily as the first mark on a blackboard.