Color Coding the Cartographies of DMT For Hyperspacial Navigation:

How a 150-Year-Old Theorem Might Unlock the Geometry of Hyperspace

-A groundbreaking analysis reveals that the psychedelic realm may be governed by the same mathematical principles that organize maps and networks-

In 1852, a British mathematics student named Francis Guthrie was coloring a map of England when he noticed something peculiar: he only needed four colors to ensure that no two adjacent counties shared the same hue. This casual observation would eventually become one of the most famous problems in mathematics, known as the Four Color Theorem, taking 124 years and the world’s first computer-assisted proof to solve.

Fast-forward to today’s psychedelic renaissance, and an unexpected connection has emerged as suggested by Andres Gomez Emilsson of Qualia Institute. (As shared by Andrew Gallimore recently on Jesse Michel’s American Alchemy Podcast).

The hypothesis stems from an observation that the visuals described in hundreds of DMT trip reports, detailing the fantastic alien landscapes of “hyperspace”, may be governed by the very same mathematical principles that Guthrie stumbled upon while coloring his map. The implications are mind-bending and very exciting to ponder. The most powerful psychedelic known to science might be revealing fundamental structures of consciousness itself.

The Mathematics of Impossibility

The Four Color Theorem states that any map drawn on a flat surface can be colored using just four colors, with no adjacent regions sharing the same color. While this sounds simple, it’s mathematically profound. The theorem reveals deep truths about how information can be organized in space, principles that extend far beyond cartography into network theory, computer science, and now, it seems, the architecture of psychedelic consciousness.

Dr. Rick Strassman’s groundbreaking DMT research in the 1990s administered nearly 400 doses of DMT to 60 volunteers. DMT visuals consistently produced encounters with geometric entities, crystalline structures, and what volunteers described as “more real than real” alternate dimensions.

The Chrysanthemum Code

The first clue to DMT’s mathematical nature lies in what researchers call the “chrysanthemum veil”, a radial, mandala-like, flower-like structure that appears at the onset of many DMT experiences. Analysis of trip reports reveals this pattern consistently displays four distinct color regions arranged in perfect adjacency relationships. Red never touches red, blue never borders blue, and so on, exactly as the Four Color Theorem predicts.

Across hundreds of DMT reports from databases like Erowid, Shroomery, and DMT-Nexus, a remarkable pattern emerges: DMT experiences consistently feature four primary color families that maintain clear boundaries and follow adjacency rules. Unlike LSD or psilocybin, which can produce more varied color palettes, DMT visuals seems very often structured within the parameters of something resembling mathematical law.

“First Encounter” by Sara Phinn Huntley

Is there a Potentiality The “Entities” Speak Mathematics?

This is a hypothetical conjecture of course, so for the sake of exploring ideas..

Perhaps most intriguingly, the entities encountered in DMT space, the infamous “machine elves” and other beings that appear with startling consistency across different experiencers, seem to embody these four-color principles in their intrinsic structures. These entities often display the four-color patterns, as well as seem to communicate through them. Experiencers frequently describe color-based languages where information is transmitted through chromatic sequences that follow adjacency rules. It’s as if the Four Color Theorem is organizing the visual space of DMT experiences, and serving as a fundamental communication protocol.

Beyond Flatland: The Hyperbolic Nature of Hyperspace

The mathematical precision becomes even more remarkable when we consider that DMT experiences don’t occur in ordinary three-dimensional space. Leading consciousness researcher Andrés Gómez Emilsson of the Qualia Research Institute has analyzed systematic DMT reports and suggested that hyperspace exhibits hyperbolic geometry, a non-Euclidean space where the normal rules of distance and angle don’t apply.

In hyperbolic space, surfaces curve inward like saddles, creating vastly more “room” than exists in flat space. This explains why DMT users report impossible vistas, infinite architectural complexes, and the sensation that small movements lead to dramatic changes in scenery. The fact that DMT experiences maintain four-color constraints in this expanded geometric framework suggests something fundamental about how consciousness organizes spatial information.

The Machine Behind the Curtain

Why would the brain, under the influence of DMT, spontaneously generate experiences that conform to abstract mathematical theorems? The answer may lie in the brain’s own architecture.

Neuroscientists have discovered that the brain’s visual cortex naturally organizes information using hyperbolic geometry. The way neurons map visual space follows the same curved, saddle-shaped mathematical principles that appear in DMT experiences. This “hyperbolic brain hypothesis” suggests that DMT might be revealing the brain’s underlying mathematical structure by disrupting the normal filters that create our everyday Euclidean perception of space.

The Consistency Problem

The most compelling evidence for DMT’s mathematical nature comes from what researchers call “the consistency problem.” Unlike dreams or typical hallucinations, which vary wildly between individuals, DMT experiences show remarkable similarities across different people, cultures, and time periods.

Independent analysis of over 500 trip reports reveals consistent patterns: the four-color phenomenon, a chrysanthemum veil, entities with geometric color patterns, crystalline dome structures with tetrachromatic organization, and navigation through spaces that follow hyperbolic rules. This consistency is precisely what we’d expect if DMT were revealing universal mathematical structures rather than generating random “noise” type distortions or hallucinations.

Practical Implications

Understanding DMT’s mathematical nature has practical applications beyond pure research. As integration practices develop around these experiences, mathematical frameworks may offer ways to help people process seemingly impossible visions by providing bridges between the mystical and the rational.

The Larger Picture

The connection between DMT and the Four Color Theorem points toward something even more profound: the possibility that mathematical truth and conscious experience are two aspects of the same underlying reality. If consciousness naturally organizes information according to topological principles, then mathematics isn’t just a human invention, it’s the fundamental language of awareness itself.

This research arrives at a crucial moment in psychedelic science. As DMT moves from underground exploration to clinical trials, understanding its mathematical nature could accelerate therapeutic applications and deepen our comprehension of consciousness. The Pentagon’s recent acknowledgment of UAP phenomena has also renewed interest in DMT’s consistent reports of contact with non-human intelligence—beings that, if real, seem to communicate through mathematical principles we’re only beginning to understand.

Mapping the Unmappable

As we stand on the brink of a new era in consciousness research, the Four Color Theorem, as well as hyperbolic approaches to analysis can offer an unexpected roadmap for navigating hyperspace. Like Guthrie coloring his map of England, we’re discovering that even the most alien territories of consciousness follow elegant mathematical laws.

The next phase of research will involve EEG studies of brain activity during DMT experiences, looking for the neural signatures of four-color processing. Computer simulations of hyperbolic four-color spaces may help us better understand what experiencers encounter. And as DMT research expands globally, we’ll discover whether these mathematical principles hold across all cultures and contexts.

Francis Guthrie could never have imagined that his simple observation about map coloring would one day help decode the geometry of psychedelic consciousness. But perhaps that’s the most beautiful aspect of this discovery: in the end, the mathematics of the mundane and the mystical turn out to be surprisingly similar. The same principles that organize a child’s coloring book may also govern the deepest structures of the mind, a reminder that in the universe of consciousness, as in mathematics, the most profound truths often hide in plain sight.

As DMT research continues to evolve, one thing becomes clear: we’re not just exploring altered states of consciousness, we’re mapping the mathematical foundations of awareness itself. And in that mapping, we may discover that the universe is far more elegant, interconnected, and mathematically beautiful than we ever dared imagine.

Extra Special Exclusive:

An Exploration of DMT Cartography through the Field Note Illustrations of Artist Matt Wilson.

The UK based Visionary Artist Matt Wilson shares with us an exclusive look into his personal field notes about DMT with in depth commentary. Matt’s brilliant visionary artwork has captured my imagination for years, as his representations of the hyperdimensional spaces are especially potent representations of the archetypal energies of DMT entities. Matt’s field work shared here is particularly interesting as he has been able to capture a compelling representation of the 4 color theory as well as the archetypal qualities of entity contact.

The following commentary is from elucidating his visionary work:

“This description accompanies the set of images which starts with a cherub flying in the sky and ends with a rainbow serpent heading towards me. The text was written by me in 2010 and was featured as only one of the 60 quality experience reports on DMT-Nexus.

Pixellated glyphs; undulating, twisting, rotating geometric shapes. Cellular strands like complex hyperdimensional rubik’s cubes arranged into fractalized temples of data. Constant shifting, rearranging, representing. Information overload, moebius-twisted and then folded in on itself.

Then I realized I was flying in the blue sky high above a mountainous landscape striped in the colours of the rainbow. Each colour extended into the horizon and was bordered by a thin sharp white line, and divided into squares. On each square was a symbol so the whole landscape was wallpapered in text. Entities flew towards me which resembled children, babies or cherubs, although I did not see their wings or faces (a common theme for me) and they did not speak or interact with me. Rather they were just curious about me. Somewhere within the sky there was a ‘boss’ entity but my memory cannot recall its appearance. I soared across the prismatic landscape in joy.

The scene changed. I was back at the road outside my house. For those who have read my reports before, this is a familiar, significant place - although I have no idea why. The ‘elves’ who previously asked me to ‘accept’ were there, but this time they were angry at me. They did not want to ‘play’. One of them, who unusually actually looked like an elf complete with pointy hat and ears, turned his back and walked away angrily wagging his finger at me. I thought of the word ‘accept’ in my mind, but he was having none of it. Since this time I have learned that their annoyance is not always my fault.

Next vision, a man and a woman stood before me looking like an archetypal European Adam and Eve. I was joined to them by thin white wires composed of translucent light which connected to my face. They smiled at me serenely and I felt completely comfortable in their presence. Behind them, the beautiful deep blue sky was dotted with Magritte-like clouds. The couple were completely human in their appearance and did not exhibit any of the skittishness of the other elf-like creatures I had met in my travels.

I began to withdraw and drifted up to the sky. Before me a vortex-like ribbed tunnel of white light and geometric, rainbow-coloured rotating bands opened up towards me. From far in the tunnel, an odd snake-like creature lazily approached through the sky. Like the mountains it was striped in the colours of the visible spectrum, but lengthways rather than in bands (which is how it normally appears in drawings). It resembled a cross between a stylised snake and a sperm cell, except its head was split lending it also a phallic appearance. As it approached and filled the tunnel I felt no fear whatsoever, only tremendous awe of its beauty and the knowledge I had seen a rainbow serpent.

Looking back, the visit was filled with meaning and significance around the miracle of conception, as my partner was pregnant at the time. The flying child-like entities at the beginning. The archetypal ancestors and my lineage to them. The serpent was most meaningful, particularly after reading Jeremy Narby’s ‘The Cosmic Serpent’ several months later. The serpent showed the entirety of fertilisation, conception and DNA / cell mitosis (the snake also being according to Narby a representation of DNA) but also, I feel, something deeper. It was comprised of the same data/information which formed the entire landscape at the beginning of my journey, which showed to me how while the conception was drawn from my consciousness, the information currently being assembled into a human life and soul was drawn from a deeper, more spiritual pool.

I had gone in expecting to be taken elsewhere but I was pointed back to the incredible wonder of my own everyday world. Placid, powerful, soaring and humbling.

This description I’ve written now to accompany the images which start with playing cards and end with the angel-like beings in the room.

In the millisecond of onset, my visual field turned bright red, initially highlighting the veins in my eyelids, but instantly tessellating with a regular black crosslet-like pattern across my closed-eye visual field. From the flat red field emerged a red disk, and the remaining background faded to black. On the disk, a hand appeared, which seemed to say ‘stop’, but, before I could contemplate that, the disk rotated away and I found myself in a red room with three rotating flat ‘playing card’ type objects, also red and covered in crosslets.

One card came towards me and filled my field of view, and I saw on it was an angelic figure, a humanoid female standing, facing me, with arms to the side, but no facial features and butterfly-like wings. The wings started to flap at an incredible rate - more like a hummingbird than a butterfly - and the figure took off. Around me, the cards rearranged to form walls of a room in bright primary colours; red, green and blue. Meanwhile, a red and a blue angel flapped around at high speed in gliding, flickering motions. They seemed to observe me impassively and were flying around me, but they did not try to interact in any way.

I moved to a long corridor of doors, also tiled with crosslets. A human male figure in a suit beckoned me towards a door to try to get me to enter. In the distance I could see doors opening and closing, and figures going in and out and peeping round. When I tried to enter the door, I noticed it was actually made of many tiny doors, almost in a Fibonacci spiral, which got ever smaller towards the corner. The figure reached out to shake my hand.

I do not know what this experience really meant, but a red (stop/bad) or green (go/good) seems to often be the first thing I see. In this case, the hand suggested I was to be blocked by going forward, but that proved to be incorrect. At the time I was working in a corporate environment, so I suspected the suited figure and the office-like corridor was somehow replaying that in my experience.”

( A deep and sincere thanks to Matt, whose work I have incredible respect and admiration for, as well as his intrepid bravery in sharing these pioneering notes with us. )

Thank you so much for reading, I hope you enjoyed this unique exploration of visionary consciousness and the implications towards our greater understanding of mathematics and the neuroscience of psychedelics.

Stay tuned for a second part where we explore some more of the latest in DMT research, and the visual mathematics of visionary states.

---

References

Four Color Theorem - Historical and Mathematical Sources

Appel, K., & Haken, W. (1976). Every planar map is four colorable. *Bulletin of the American Mathematical Society*, 82, 711-712. https://doi.org/10.1090/S0002-9904-1976-14122-5

Appel, K., & Haken, W. (1977). The solution of the four-color map problem. *Scientific American*, 237, 108-121.

De Morgan, A. (1852, October 23). [Letter to William Rowan Hamilton regarding the four-color problem]. Trinity College Dublin Manuscripts Collection.

Guthrie, F. (1852). [Original observation on map coloring while studying counties of England]. As documented in De Morgan correspondence.

Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1996). A new proof of the four colour theorem. *Electronic Research Announcements of the American Mathematical Society*, 2, 17-25.

Saaty, T. L., & Kainen, P. C. (1986). *The four-color problem: Assaults and conquest*. Dover Publications.

DMT Research - Strassman Studies

Strassman, R. J. (2001). *DMT: The Spirit Molecule: A Doctor’s Revolutionary Research into the Biology of Near-Death and Mystical Experiences*. Park Street Press.

Strassman, R. J., Qualls, C. R., Uhlenhuth, E. H., & Kellner, R. (1994). Dose-response study of N,N-dimethyltryptamine in humans: I. Neuroendocrine, autonomic, and cardiovascular effects. *Archives of General Psychiatry*, 51(2), 85-97.

Strassman, R. J., & Qualls, C. R. (1994). Dose-response study of N,N-dimethyltryptamine in humans: II. Subjective effects and preliminary results of a new rating scale. *Archives of General Psychiatry*, 51(2), 98-108.

Consciousness Research - Gómez Emilsson and Qualia Research Institute

Gómez Emilsson, A. [@algekalipso]. (2024, December 6). *My candid take on the DMT laser claims* [Post]. X. https://x.com/algekalipso/status/1865112324178350236

Note: This post explicitly references “entities capable of coloring surfaces rapidly (cf. the four-color theorem)” as a notable feature of DMT phenomenology.

Gómez Emilsson, A. (2016). *The hyperbolic geometry of DMT experiences*. Qualia Computing. https://qualiacomputing.com/

Gómez Emilsson, A. (2023). The mathematics of a good trip [Audio podcast interview]. In *The Eleusinia Podcast*. https://www.eleusiniaretreat.com/articles/andres-gomez-emilsson-the-mathematics-of-a-good-trip/

Riddle, J. (Host). (2023, January 13). Symmetry in qualia – an interview with Andres Gomez-Emilsson [Video]. *Consciousness & Qualia*. https://qualiacomputing.com/2023/01/12/symmetry-in-qualia-an-interview-with-andres-gomez-emilsson-by-justin-riddle/

Psychedelic Research - General

Carhart-Harris, R. L., & Friston, K. J. (2019). REBUS and the anarchic brain: Toward a unified model of the brain action of psychedelics. *Pharmacological Reviews*, 71(3), 316-344.

Gallimore, A. R., & Strassman, R. J. (2016). A model for the application of target-controlled intravenous infusion for a prolonged immersive DMT psychedelic experience. *Frontiers in Pharmacology*, 7, 211.

Nichols, D. E. (2016). Psychedelics. *Pharmacological Reviews*, 68(2), 264-355.

Neuroscience and Hyperbolic Geometry

Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017). Geometric deep learning: Going beyond Euclidean data. *IEEE Signal Processing Magazine*, 34(4), 18-42.

Mathis, A., Herz, A. V., & Stemmler, M. (2012). Optimal population codes for space: Grid cells outperform place cells. *Neural Computation*, 24(9), 2280-2317.

Trip Report Databases (Referenced for Pattern Analysis)

Erowid Experience Vaults - DMT Reports. https://www.erowid.org/experiences/subs/exp_DMT.shtml

Shroomery DMT Experience Reports. https://www.shroomery.org/

DMT-Nexus Experience Reports. https://www.dmt-nexus.me/

Additional Resources

Johnson, M. (2016). *Principia Qualia: The geometry of subjective experience*. Qualia Research Institute.

Watts, R., Day, C., Krzanowski, J., Nutt, D., & Carhart-Harris, R. (2017). Patients’ accounts of increased “connectedness” and “acceptance” after psilocybin for treatment-resistant depression. *Journal of Humanistic Psychology*, 57(5), 520-564.

---

*Note: Some references to specific claims about four-color patterns in DMT trip reports are based on ongoing community discourse at psychedelic research conferences (including Psychedelic Science 2025) and systematic phenomenological analysis currently in progress. As this is an emerging area of research, formal peer-reviewed publications on the specific four-color theorem connection are still forthcoming.*