CHRONOS & CHAOS #12, Dodecatemoria: Ancient Fractals in the Zodiac
- Joey Cannizzaro
- Mar 9, 2024
- 11 min read
Updated: Mar 10, 2024
Dodecatemoria are divisions of each sign of the zodiac into 12 equal parts, each of which is occupied by a different sign in zodiacal order. In this way, inside the 30 degrees of each sign is contained the entire zodiac in miniature. Each 2.5 degrees of a sign is the entirety of another zodiac sign, starting with the sign itself. So picture Aries: it has 30 degrees. The first 2.5 degrees are another layer of Aries, then the following 2.5 are Taurus, the following Gemini, the following Cancer, all the way to the last 2.5 degrees that are occupied by Pisces.
This idea goes back to ancient times, and dodecatemoria (also called twelfth-parts, duads, or in Jyotish astrology Dwadasamsa) were used by most of the Hellenistic astrologers including Valens, Ptolemy, Dorotheus, Paulus, Rhetorius, Porphyry, Hephaistio of Thebes, and Firmicus. Several authors enjoin us to consider them central to the practice, like Rhetorius, who says that, “the method of Dodecatemories is a necessity in nativities; and I also put down the astrological significations of these so that some might use them not just as in a secondary work” (Rhetorius, Ch. 18, Holden trans., 2009, p. 18) or Firmicus, who asserts that, “some think that they can find the entire substance of the nativity from them, and they intimate that whatever is concealed in the delineation can be discovered from the dodecatemories.” (Maternus, Firmicus. Book II, Ch. 17 , Holden trans., 2011, p. 59)
Still, at first I was resistant to the idea of dodecatemoria because it seemed like an additional (confusing) rulership scheme. There are many different ways of breaking up every sign into sub-rulerships: domicile & exaltation lords rule the entire sign; the bounds break each sign up into 5 parts, each with a planetary ruler; the decans break each sign into 3 sections each ruled by a different planet. But signs do not rule planets, planets rule signs. So how and why would there be a segment of each sign occupied by one of the other zodiac signs?
It turns out that dodecatemoria are not a rulership system at all. They are more like fractals of the chart infinitely receding into each sign, like 12 chambers of a nautilus shell.
Every planet and point in your chart falls not just in its own sign, but in a section of that sign which is inextricably connected to a different part of the chart. However, the dodecatemorion is not just 2.5 degrees of that sign: the entire 30 degrees of the sign is compressed within it’s particular 2.5 degrees of each other sign, so if your sun is at 3 degrees of Ares, that is also the dodecatemoria of Taurus, and it falls at about 6 degrees (1/5th of the way through the 2.5 degrees of Taurus’ dodecatemoria in Aries). In this way, dodecatemoria don't just add one more rulership on top of the sign—the entire sign is grafted onto that 2.5 degrees of space, along with all of its rulerships (domicile, exaltation, triplicity, bounds, decans, etc). Hellenistic astrologers would often check who the bound lord is of the particular degree of the dodecatemoria of someone’s ascendant.
Don’t worry about the math if it sounds baffling (there are online calculators), but it’s easier to picture it visually; it’s easier to understand it as what it is: a fractal.
From the "Mandelbrot Set" a simple mathematical formula that produces infinite fractals
“A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole."
Dodecatemoria are definitionally fractal. Since the astrologers who historically employed the technique don’t provide much philosophical context for their inclusion in the system, the better question to ask in figuring out how to actually use & interpret them is: what is a fractal, and why did every major Hellenistic astrologer incorporate them into the wheel of the zodiac?
The idea of macrocosm & microcosm is an integral part of the Hellenistic understanding of astrology & why it works. The Stoic concept of cosmic sympathy is one articulation of this idea: that all the things of the world are an expression of one or more of the planetary deities, just on radically different scales. As the philosophy that justifies & explains the correspondences, it’s a foundational part of the philosophical grounds for astrology, but macrocosms and macrocosms aren’t anywhere graphed or visualized in the chart, except in the dodecatemoria, in the form of fractals.
Fractals aren’t just a mathematical construct. As Benoit B. Mandelbrot demonstrated in his seminal 1982 book The Fractal Geometry of Nature, fractals are ubiquitous throughout natural objects, not just abstractions. (Check out Mandelbrot’s TedTalk on the mesmerizing topic.)
Snowflakes are the most famous example: every snowflake is a unique shape, but it is made up of innumerable smaller snowflakes of the same shape, so that even when you look under a microscope, you will see the form repeated on the microscopic scale. Bizarrely, fractals don’t only appear in one material or form of matter. Rivers running to the sea also create fractal patterns, as do coastlines. The leaves of many plants have fractal geometry, perhaps most famously ferns. Each leaf of a fern is the shape of the larger plant, and each of those leaves has small leaves on it of the same shape, repeated, and repeated.
Mandelbrot’s mathematics, and their capacity to identify a pattern in perceived chaos, have had a massive material impact. Fractals are now used to predict hurricanes, earthquakes, volcanic eruptions, floods, and wildfires. CGI natural environments were impossible to fabricate before Mandelbrot came up with his method of quantifying natural geometry. They’re being used to understand and adapt to turbulence in air & water. The human lungs & other branching organs are fractal, so they’ve become integral to medical research. While the entire universe is not itself a fractal (as Mandelbrot suggested) the distribution of galaxies does follow a fractal pattern and this has been used to accurately predict the location of far away galaxies. They are present throughout the cosmos, for example in “clumps of dark matter called "halos," which host galaxies and their clusters, form nested structures and substructures, with halos holding sub-haloes and sub-sub-halos inside those.”
By introducing fractal geometry into the natal chart, a sort of “chaos” is created in trying to connect seemingly disparate parts of the chart to each other (symbolically & interpretively). The dodecatemoria are the fractal pattern within this chaos that enables us to see irregular order & beauty within that perceived disorder. The entire rest of the ancient astrological system is tight, orderly, and in many ways symmetrical. Is seems that dodecatemoria are the tool Hellenistic astrologers used to re-introduce some of the awe-inspiring chaotic order of nature into the astrological system. If the aspects represent pythagorean geometry, divine order, the dodecatemoria are the only part of the system that also incorporate all the other forms, the irregular geometry of nature that is actually far more ubiquitous than regular shapes.
According to Dr. Ron Eglash’s article "Fractal Geometry in African Material Culture," fractal designs are widespread throughout Africa, and were present in ancient Egyptian architecture & art. It’s hard to imagine that a society whose survival depended on a massive river delta wouldn’t attach cosmological significance to the fractal pattern which inevitably formed each year as nutrient-rich silt was deposited in the Nile flood plains. What explicit influence this had on the colonizing Greek culture and their nascent astrological system isn’t clear.
One version of the idea that the Hellenistic astrologers would certainly have been directly familiar with is Zeno of Elea’s paradox to disprove plurality. Written in the 5th century BCE, Zeno posits that if there is more than one thing, there has to be something that separates one from the other, but if that’s the case, there must always be something else in between the thing that separates those two things as well, and something else between the thing that separates the separator, ad infinitum. In this way, if there are many things, there must also be only one thing, receding infinitely. This paradox of individuation within ultimate unity is exemplified by the dodecatemoria: each of the degrees of the zodiac are not separated by empty space, but by an entire other zodiac, and zodiacs between those zodiacs, forever.
Alan Watts, in his writing on Taoism, discusses the non-confuscian Chinese philosophical concept of Li. The word translates literally to the grain in jade. “It also means the grain in wood and the fiber in muscle. We could say, too, that clouds have li, marble has li, the human body has li… when you look at a bamboo plant, it is perfectly obvious that the plant has order. We recognize at once that it is not a mess, but it is not symmetrical and it is not geometrical.”
This particular kind of beauty, the recognition of something divine & right in the mess of something natural, is precisely what should guide our interpretation of the dodecatemoria in astrology. Taking the natal chart & adding the fractal layer of dodecatemoria is like adding the woodgrain back to a blank board; the wild quality of a natural thing exists in the space between a point or planet in your natal chart and it’s dodecatemoria somewhere else in the chart. The practice is in trying to comprehend (and draw interpretation from contemplating) how that part of Cancer, for example, could also be a different segment of Aries, how both signs express each other’s qualities, or iterate the same pattern.
It’s as though each dodecatemorion proposes a paradox, and the answer is your delineation. It may help to phrase it in the form of a paradox, so for example, if the person has their moon at 15 degrees and 1 minute of Sagittarius, the paradox would be:
15°01 degrees of Sagittarius is 0°15 Gemini
The formula is:
_____________________________ is ____________________________
[degrees of natal planet or point] [degree of its dodecatemorion]
The only time this doesn’t work is when you have a planet in the first 2.5 degrees of a sign, because the dodecatemorion will be the same sign as the original planet/point (though it will still be at a different degree unless the planet is at exactly 0 degrees & 0 minutes of the sign, in which case the planet’s lack of an alternate iteration is the message).
Many of Hellenistic techniques that actually employed dodecatemoria seem to indicate that you would use them to discover something when no other known method could provide that information. As Firmicus says, they reveal “whatever is concealed in the delineation,” giving mystical significance to the act of looking in this way. Valens’ use of them to identify the ascendent of those without a time of birth seems absurd if you take it at face value— Valens would have known that the technique doesn’t work by checking it on any chart with an accurate time. This indicates that the technique only works if the information is unknown or hidden. This resonates with the esoteric nature of the tradition & the transmission of astrological knowledge. This is a much more compelling explanation for Valens’ inclusion of the technique than the idea that he simply didn’t bother to check if it worked.
One final note on what unique tools the fractal of dodecatemoria provides us: fractals are fundamentally a matter of scale. When is it useful to be able to change the scale of the chart to discover more information? One key application of dodecatemoria is in the study of the charts of twins. On the macro scale of the chart their difference in birth times can seem to have an almost negligible effect on the chart. But magnify by one power using the dodecatemoria & you have two completely unique charts for those twins, with different placements for the AC, moon, sun, MC, and Lot of Fortune. Below, first you’ll see the twelfth-parts of my chart & then the chart of someone born only one minute after me. If there is even a 1 minute difference between two events in time, you could use dodecatemoria to produce echoes of their charts on different scales, so even if the first level of dodecatemoria are very similar, the 2nd or 3rd level inevitably grow more & more distinct. Dodecatemoria can be a practical (potentially infinite) microscope for peering into the cracks of the chart, and the cracks behind those cracks, and the cracks behind them.
My dodecatemoria chart
Dodecatemoria chart of imaginary twin born one minute after me
If you want to try and work with dodecatemoria yourself, I recommend that you start with your own natal chart. You can go to Astro-seek.com > Free Horoscopes > Traditional Astrology Calculator and put in your birth data and it will show you a list of the dodecatemoria of each of your planets and chart angles. Choose a planet that you’ve always found hard to identify with or hard to see in your own personality, or one that you struggle with the archetype, or one whose themes you wish wouldn’t keep resurfacing in the same way in your life. Look at the dodecatemoria of that planet, and try to work out how that part of yourself might in some way express itself with the energy of that other sign. See if there isn’t some backdoor connection there that could demonstrate some other way of being, or give you advice about another path to take.
Imagine for example, that someone has always wanted to write but can’t get themselves to actually do it. Let's say they have Mercury in the 12th house in Pisces (the planet of communication in its sign of detriment & fall, in the house of invisibility). You can check the dodecatemoria of their Mercury to see if there’s some other pathway, some alternate-world version of their Mercury that can assist them. Maybe it’s in Aquarius (their natal 11th house of friends) conjunct their natal Venus, so you suggest they join a writing group instead of trying to force a solo practice, or co-write on the same document with someone, or work with AI language generators, or maybe try a more experimental (Aqua) or stylized (Venus) approach. This is a simplified example, but there’s incredible potential in weaving together & creating a dialectic between these portals in the chart.
I’m so excited to feel like I finally have an understanding of the role of dodecatemoria, both where they fit in the astrological system and what they represent in the cosmology that the zodiac wheel graphs visually. Without the missing piece of fractals, I think many struggle to articulate what the point is of the dodecatemoria, and how exactly to use them to get to meaningful interpretation, beyond just “look at them for extra info.”
This process of researching and writing about dodecatemoria has, for me, clarified an approach we can take as traditional astrologers: even if Ptolemy or Dorotheus or Paulus didn’t provide their rationale for a technique or a part of the system, we can study the technique itself to understand it’s metaphysical role in the larger system, and from that determine a practicable means of working with it that doesn’t disregard the tradition, but also doesn’t limit itself to only working with fragments of explicit instruction from ancient authors. By studying fractals themselves, which have been observed and contemplated forever, but only named & theorized in the last few decades, I was able to construct a methodology for putting this ancient technique into action without straying at all from how dodecatemoria were historically used in the practice. Instead, I elaborated an interpretive principle from the historical practice itself. It’s incredibly exciting to know that the more I learn about and understand fractals, the more that will inform my practice with dodecatemoria as an astrological tool.
I hope you’ll send me a message & tell me if you make any discoveries or have any insights while looking at your own charts! I’ve also found some uncanny connections when looking at the dodecatemoria of my chart and comparing that to the charts of people in my life. For example the dodecatemoria of my AC is conjunct an important point in every one of my past partners charts (and I have nothing in that part of the natal chart). Check this out too and let me know what you find!
SOME DIGITAL RESOURCES:
Astro-Seek has a Traditional Astrology Calculator so you can calculate your dodecatemoria
Seven stars astrology is an indispensable resource for Hellenistic & other traditional astrology. This is one of the best online articles on dodecatemoria.
Rok Koritnik contributes a lot to the topic as well, including comparative analysis between Jyotish and Hellenstic approaches:
Professor Ali Olomi is doing dyamic work with dodecatemoria (though you'll need to subscribe for access).
This Reddit thread on r/advanced astrology is informative:
Snowflakes photographed by Don Komarechka.
"Lightning" art by Bert Hickman
