FORGET WIKIPEDIA on the Axial Age, it is completely useless.
I fear the notion of the Axial Age has fallen into confusion.
In the eonic model of the eonic effect we see what are essentially three transitions equally spaced and about three centuries in length. The second is sometimes called the Axial Age, but the only clear case is completely secular, the Greek transtion, as archaic Greece most remarkably starts to take off in the period after -900.
Keep in mind that the emergence of religion in the Judaic ‘Axial’ is misleading. The concept of monotheism arises, slowly, crystallizing ca. -600 (in part influenced by Zoroastrianism also) in the context of a tribal/state culture and its theocratic religious beliefs. Many of the elements of later religion begin to emerge. But our idea of religion, e.g. Judaism, Christianity, Islam, are NOT Axial creations. This requires therefore careful use of the term ‘religion’.

The issue of the non-random pattern then is of three transitions over five millennia from Egypt/Sumer to modern times. The clustering of innovations in these transitions is what creates the overall non-random pattern.

I need reminding that the idea of the Axial Age is hopeless confusion in most people’s minds. I rarely used the term in the first edition, but allowed it in in the second and third, but in the final analysis the analysis of the eonic effect has to mention and then set aside the terminology of the Axial Age.
I have discussed multiple times the confusion sown by Karen Armstrong on this question, along with many others on the internet. The Axial Age for me is simply a vague reference to the brief interval of generative innovation that brings into existence a new age of world history, between -900 and -600, with an aftereffect of about two centuries, to -400, as the new explodes into form. That’s something far more than the question of religion, which has confused the issue. Israelite culture in this ‘Axial’ transtion produced prophets, and tended to critique its polytheism, just as the modern Enlightenment in the modern transition critique monotheism. The overall pattern of culture was not religion generation in our sense. All that we consider religion now arose in the wake of the Axial Age.

It is much better to study these issues with the Greek example where the issue of Axial Ages producing religions doesn’t even arise.

By “Axial age,” I am assuming your talking about a point in history 2000 years ago, or so, where civilization first emerged with the worlds religions?

See this link:

http://en.wikipedia.org/wiki/Axial_Age

And by the “non-random pattern,” I am assuming you are talking about the way religion emerged with civilization all over the world and all at once? The pattern show a break in the deterministic chain that points to the past? Hense, evolution and history show two faces? And so we can infer that something is holding the two together as one evolution?