[Edited gently for clarity January 2017]
There are two major contenders for the source of the geomancy’s dispersion in the last couple of millenia: West Africa or the Middle East. It is quite possible that neither are the final origin, that a still older cultural substratum pre-exists both. What we can say about that older substratum, if it exists, will nonetheless require us to pass through its more recent points of transmission.
There are many geomantic techniques in West Africa, so that makes it a reasonable claimant. There is Ifa among the Yoruba, and the Nupe, the Dahomeans, the Bamani, the Edo, and others all have clearly related geomantic divination systems rooted in four unit signs with each unit occupied by one of two binary elements. And that is to say nothing of the distribution of definitively Islamic geomancy in the region.
But there are also many marks against West Africa as origin. First and foremost, many West African practices have only a minor mathematical component. Dahomean Fa and Yoruba Ifa are good cases in point. While there are 16 signs that parallel exactly the 16 signs of Islamic geomancy, those signs are deployed as a narrative cataloging system rather than as a mathematical system.
The Fa/Ifa practices begin by producing a primary sign, almost like defining a section in a library, and then you proceed to take a secondary sign to narrow down the search to specific myths and ritual practices. There are mathematical elements, but they are not primary to the work. Considering how basic the math is to the structure of the system, it seems unlikely that the system would have originated first as a cataloging system and then become mathematical (I owe the mathematical observations to Louis Brenner’s “Muslim Divination and the Religion of Sub-Saharan Africa”).
The second and related point is a matter of distribution. Geomancy spread so readily because it combined a simple yet powerful mathematical structure with an equally simple yet rich symbolic network. Those features aren’t present in practices like Ifa and Fa, which instead rely on feats of memory (oh, but what feats!) and spiritual communication to function; neither of those travel quickly. Meanwhile, following the coast of West Africa up and around into the Mediterranean region and down along the Eastern coast of Africa, you find all kinds of broadly geomantic systems, all along the zones of contact between rapidly expanding Islamic kingdoms and trade networks.
Of tangential but not insignificant interest, I want to point out that in the Ifa corpus there are stories that assign geomancy first to Shango who later traded to Orunmila for drums and dancing. J. Lorand Matory points out that that there are praise songs that describe Shango as a heterodox muslim, as one who has gone on pilgrimage to Mecca. Perhaps from which he brings the gift of geomancy? Very speculative, but not entirely out of the scope of possibility.
You also don’t see any good evidence for there being an indigenous Bantu practice of geomancy. The Bantu departed from the West African region prior to Muslim contact and seem to have nothing like geomancy in their deep cultural repertoire (though Bantu practices in the Americas seem to readily acquire and develop geomantic practices). This is only weak and indirect evidence toward my support of an Islam-driven distribution. The practice of geomancy could have developed in the time between Bantu out-migration from West Africa and Islamic contact with it. It just seems increasingly less likely that it could have both developed and dispersed so broadly in that narrower window.
(You also find something parallel to Ifa in terms of its conversion of mathematics to mnemonics in the Caroline Islands where a system of 256 signs, composed of interlocking units of 16 core signs, is used for sacred divination. Weird and wonderful, reputedly brought by a stranger who had become separated from his boat. I don’t have a good explanation for that, only a bunch of more and less wild speculations.)
As a third point, in early records (10th century-ish A.D.) of Islamic missionaries and merchants to West Africa, you find no mention of a tradition of geomancy, though you find some allusive references to geomantic-like sand cutting closer to the Islamic Mediterranean. Also (thanks again to Louis Brenner) we have an interesting linguistic quirk. In Arabic, when geomancy is done by marking dots in sand, it is called khatt ar-rhaml, and ar-rhaml sounds an awful lot like ‘Orunmila,’ who is credited with the Yoruba practice Ifa. (Oh, and yes, the traditional table on which Ifa divination is done has its antecedents in wooden boards covered in sand used to teach children lessons in early Islamic schools.)
Okay, so this is moving toward answering what favors an Arabic origin in place of a West African one. The system of geomancy as it entered into the European world had clear ties to astrological lore. Astrological lore, with its deep roots in places like Sumer and way back into Gobekli Tepi, suggest there might be more than an accidental association between the two. Second, the practice in Islam is associated with Idris, under whose auspices Islamic scholars incorporated much of what we tend to identify as the Hermetic corpus. (Idris is identified as the ‘real’ basis for Thrice-Great Hermes in various points in Islamic intellectual history.)
The way in which the Hermetic material was able to acquire at least a passing appearance of orthodoxy for some medieval Muslims makes it a stronger candidate for having entered into popular use and been able to be rapidly transmitted through trade and conquest routes, in a manner that practices drawn from the hinterlands would not likely have achieved.
(Bernard Maupoil, while studying African geomancy in the mid-twentieth century, also observed that there seemed to be a residue of astrological lore and rites in the material, suggesting once again that what we see in West Africa results from a radical and amazing West African appropriation of geomancy to new ends rather an an invention that spread outward from it. I am always startled by how hesitant some people are to suggest that people in Africa might have been brilliant innovators as well as as originators.
Other communities like the Dogon and Dagaara are interesting to consider on the astrology-geomancy front since they, too, have overlapping systems of geomancy and astrological lore, though they aren’t as well-discussed as their more coastal relatives; the sound and fury around Marcel Griaule has muddied a lot of waters, though. )
There is little doubt that the European practices of geomancy came out of contact with the Islamic world. Not only do we have intimate ties between the Islamic world and Spain, more than a few Reformation-era Protestants spent time in the Arabic world which was generally more congenial to them than the Catholic atmosphere of Europe. More than a few Protestant reforms seem to have been modeled, in part, on their admiration for the cosmopolitan world of their Islamic hosts. I suspect, too, that a subset of the early modern grimoires have ties to these channels as well.
So, where does that put the origins of geomancy? It’s still hard to say for certain, but it suggests that it lies in the Middle East broadly construed, likely predating Islam, though spreading out rapidly and opportunistically under its influence. I would suggest that one of the likely centers lies somewhere in the Sabean/Mandean/Harranian/etc. mesh of practices, some of which became part of the early and more heterodox mystical orders of Islam from which more respected and orthodox Sufism would emerge.
There are also some strong parallels between geomancy and the I Ching, and you can easily label one ‘Middle Eastern geomancy’ and the other ‘Chinese geomancy.’ If we are looking for a deeper source of geomancy proper, I would start with seeing if we might be able to triangulate it by seeking the point of their mutual divergence toward their own quite distinct, but distantly related, forms. In other words, if there might be a geomantic roots we can only hypothesize after, akin to how we grasp at proto-Indo-European language.
Here I’m thinking about the roots of the I Ching being tied to the cracking of shell or bone (subtle necromancy there) in a fire, the primacy given to the fire line in geomancy, and the antiquity of Zoroastrianism’s fire reverence. Speculative, yes.
Also, there is a simplified form of geomancy that has signs composed only of two units rather than four which I have found, quite disparately, described in use both in China and the Upper Volta region of Africa. The two units generate three signs, which mean, in both places, yes-no-laughing. Again, I have no good explanations of this, but a simpler form preserved in disparate places suggests we might be seeing a tiny bit of proto-geomantic grammar or phoneme. How weird and wonderful is our world sometimes, when it isn’t all about the stabbing and the screaming?
This is all starting to feel a bit like Dictionary of the Khazars writ on a still larger scale, no?