Non-expert ideas, but since this question has been up for a couple of days, here are some thoughts..

Although this sounds like a straightforward question, really I think this question unravels into what's been called the 'Laplacean spirit'. Either that, or the terms wind up recursively redefining themselves.

If it were possible for human understanding to raise itself to the
ideal of the Laplacean spirit, the universe in every single detail
past and future would be completely transparent. "For such a spirit
the hairs on our head would be numbered and no sparrow would fall to
the ground without his knowledge. He would be a prophet facing forward
and backward for whom the universe would be a single fact, one great
truth." And yet this one truth would present only a limited and
partial aspect of the totality of being, of genuine "reality." For
reality contains vast and important domains which must remain forever
and in principle inaccessible to the kind of scientific knowledge thus
described. No enhancement or intensification of this knowledge can
bring us a step nearer to the inner mysteries of being. -Cassirer, 'The Laplacean Spirit'

Also, I think *perfect ontological chaos* entails *perfect epistemological chaos*.

Firstly, I would think perfect ontological chaos would entail an infinite domain.

Assume an unchanging binary sequence 1011. Assume we consider it as a closed system, then we might reconfigure our own interpretative system to give it order:
'First half is opposites; right side is all 1s'.
Or we might say,
'Alternating sequence, except for last item'.
We can collect up all of these interpretations to give the required information resources of the observer system, and the information associated with the observed system. In any case, the information content will obviously be finite, and therefore we have not reached perfect chaos.

Likewise, if we consider this a peek into a larger system, such as ..1011.. , then we still will develop strategies for defining the extension of our knowledge. Strategies that would extrapolate this in unusual ways would be weighted low; obvious strategies would be considered likely. For instance, if we flip a coin a hundred times in a row, and it comes up heads every time, we would expect it to be a trick coin, and therefore would guess heads on a fair toss; our strategy would be 'heads'. In any case, let's just assume our observer system is not 'perfect chaos'. I think a strong argument could be made that perfect chaos cannot 'observe' or 'make meaningful representations'.

I also propose that the 'unchanging binary sequence' example can be generalized to any finite system under observation while maintaining these conclusions.

So now, in order to approach infinite information, we must approach infinite resources for storing our interpretive program and the data under consideration; therefore perfect chaos entails infinite domain.

Now, if we are dealing with an infinite domain but consider ourselves finite 'strategies', then we can only observe this infinite domain partially at any given time. We must make assumptions as we go, but we cannot make sense of it, therefore perfect ontological chaos entails perfect epistemological chaos.

To show this in better detail, let's say that, as we go, step by step observing, we constantly restructure our strategies. Our strategies might make sense to us for some steps, but over all steps, the information content must be infinite. In this case, it doesn't matter that things made sense 'in the moment', and that we were able to handle them with our finite resources, we can be assured that we cannot in the full scope fall back on old information. Whether we actually can experience infinite 'steps' is a question for Zeno, Planck, or spiritualists. In this case, we may be 'saved' from the possibility of perfect chaos by our own finitude.

Either that, or we might redefine perfect chaos to be the maximization of disorder related to one's own perceptual system. But then it no longer seems a philosophically pregnant term.

Our perceptions have a great ablility to 'scope' information, such as when a complex rhythm played quickly enough becomes a 'timbre', and also to link perceptions together, such as when moving images kick in proprioceptive feelings.

2Can I push on the definition of "perfect chaos?" The word has many meanings, and which meaning you choose will shape the answers. Consider the mathematical definition of chaos actually has some order to it (in the form of stable orbits). Mathematically pure-randomness has no order, but it subject to the Central Limit theorem (which leads to what you see as bulk properties). I bring these up because Nietzche's definition of chaos is less exacting than the mathematical version, and if you are talking about "perfect chaos," exacting definitions become helpful. – Cort Ammon – 2015-01-20T16:43:08.893

@CortAmmon: Sure; is there a mathematical chaos that has neither order in its 'micro-structure' or in its 'bulk-structure'? Nietzsches imprecise, because he's talking in very generally terms; and not about mathematics but about matter; so his necessity is determinism broadly construed. – Mozibur Ullah – 2015-01-21T13:27:57.053

The closest I can think of to that definition is Basyean inference with a Jeffries Prior, which I believe can be phrased as claiming not that the world is unordered, but rather that any ordering that may exist is unknown. Is that starting to approach a direction which is reasonable for starting an answer? – Cort Ammon – 2015-01-21T15:47:58.627

@CortAmmon: Its closer; but I'd put it as 'epistemological perfect chaos' rather than an 'ontological perfect chaos'; I think its the second which I'm after; its worth pointing out that N doesn't think its possible given his assertion above. – Mozibur Ullah – 2015-01-22T10:34:16.030

he doesn't mean chaos per se, else there would be no repetition surely ? – None – 2015-01-23T06:02:33.887