Worldbuilding: Spell Maps and Magic Systems

Despite this being the Occult Triangle Lab, I haven’t spoken much about occult trigonometry. I’ve talked about using binary code as the basis for magic systems, as well as magic as poetry, but not much to do with triangles. Except for that origami pyramid wrapped up with Zen.

The origami pyramid Nirodha.

Magic in fantasy, as I’ve said before, shouldn’t be a science. It shouldn’t be a palette-swapped form of electricity or physics, where mages carry out “experiments” like Isaac Newton (though he himself was apparently a big fan of alchemy). The reason is that magic, when approached like a science, brings up same reductionism that haunts modern people: if we’re all just chemical reactions in our brains, is there space for truth, or meaning, or wonder? Because those are the very things fantasy can explore like no other genre.

I think magic in fantasy should have rules. The way I conceive it, it should undergird the workings of nature and the world, similar to how Ursula LeGuin’s used taxonomy as magic. But when I imagine magic, there’s something transcendental about it that goes beyond science and materialism. How do you begin designing a system like that? It’s like making up a fictional branch of aeronautics. But that’s what’s so amazing about worldbuilding: you get to make the rules.

What follows is the basic building blocks for a magic system that I conceived back in 2014, combining the art of Buddhist mandalas, computer coding, and musical theory with metaphysics, astronomy, and trigonometry. This is, in the realest sense, a product of an occult triangle lab. One note, however: this is all hypothetical. I don’t have a degree in linguistics like Tolkien, or in graphology. To actually create the symbolic language I describe and to embed these kinds of patterns in it would be something akin to making a crossword puzzle out of an entire language. It would take years of careful construction. So maybe a long-term project for me.

But in the meantime…


A couple years ago, I started to sketch out the beginnings of a written magic system for my fantasy world. I imagined putting together a bunch of symbols in a sequence that expresses what you want to happen, like you’d do with a line of computer code. But there is something inherently beautiful about how these symbols would fit together: if you deconstruct the interactions between the symbols, you would find that all the symbols could be grouped into discrete units, with the groups’ unity based around shared markings in their graphic composition (similar strokes and dots in the symbols) or the part of the spell they affect (such as binding or flight). These rows of symbols would form rectangular paragraphs, and these rectangles could be oriented to one another like building blocks to form geometric shapes, with each paragraph forming a side of the shape.

occult triangle lab chris mahon worldbuilding fantasy spells

These shapes would be arranged into a “spell map,” a geometric representation of how the different parts of the spell work together. It would form a radial or symmetrical design based around a central polygonal figure, such as a square or hexagon. Arms extending from the central polygonal shape would represent the different aspects of the spell, and the smaller components of the arms would be based around their own geometric patterns, making a chain of hexagons, squares, triangles, and so on. So the patterns contained within the individual lines of magical code would eventually form spirals of meta-patterns.

A functioning, well-written spell would have perfect symmetry when all the symbols are arranged in this manner, so a mage writing a new spell could actually lay out their writing in a half-made spell map and figure out what to write next based on their knowledge of geometry and angles. They can also figure out where their spell is going wrong based on the symmetry of the design.

Spell Maps, Triangles, and Designa

The thing is, every polygon is made up of triangles. When you have a regular polygon, like a pentagon, you can subtract 2 from its number of sides and multiply that by 180 to get the sum of its internal angles. Why 180? Because that’s the sum of the angles in a triangle! If you’re trying to create huge, perfectly geometrical spiral designs, the key lies in the shapes that will work well with the central polygonal shape; linking together a hexagon and a pentagon will make for some crowded, chaotic spiral arms. Shapes made from the same sort of triangles that make up the central polygonal figure, on the other hand, might work to create perfect mandala-like designs.

Working with triangles as the basic building block of all shapes, you can figure out the angle measures of the “ideal” triangle for your central polygon (say, a hexagon, which is made up of equilateral triangles with angle measures of 60 degrees) and create a grid made entirely of those triangles. Using this grid, you can be assured that all shapes made from those triangles will have angles measures and lengths that will synch well together. If you’re a mage, it also means that you have all routes for the development of a new spell map.

occult triangle lab chris mahon worldbuilding fantasy spells
But in practice, single-triangle grids may not contain all the triangles necessary to create perfect designs, especially if you want a mix of different shapes. You’ll need permutations of the right triangle, the equilateral triangle, and 30-60-90 triangle, with angles and lengths adjusted to fit the angle measures of your central polygonal figure to have all possible options. This means, to see all possible shapes, you should be working with three triangles grids superimposed on top of one another, calibrated to the right angle measures.

So that’s where things get complicated.

A book I picked up from The Strand is a great guide to this kind of geometrical drafting–it’s called Designa by Wooden Books, and it walks you through the history, drafting techniques, and mathematics behind different designs from all over the world, including Muslim religious patterns and Celtic knots. Woven into these patterns are symbolic meanings and symmetries, reflecting beliefs about the universe, nature, and God.

So there you have the first stage: the idea of a spell map, a meta-pattern that gives a geometric structure to a normally linear, code-like spell made of symbols. Like a computer system, it can be revised and troubleshot based on the patterns embedded in its operations. When it’s evoked, it casts the spell coded into it.


After looking at the triangular grids I’d made, I used the horizontal lines made naturally when you mirror two rows of triangles vertically to measure the size of a map, which would express its “magnitude”: the larger and more complex the spell, the more space on the grid it will require, and the greater its “magnitude,” since larger spells means using more lines of symbols. And that led to a new idea.

As I looked at the designs I’d made, I wondered what it would look like if I tried to reduce all of the symbols and patterns to binary, so that a spell could be fed through a punch card-computer, like UNIVAC. I also realized that the “magnitude lines” I’d drawn also imposed something like a musical staff on the whole design. It reminded me of Deadmau5 playing the Castlevania theme on a bunch of modular synthesizers, and the Black Midi series, especially this one, where the designs made by the notes end up looking like large spell map. I imagined playing cross-sections of a spell map like Black Midi, with every symbol being a note.occult triangle lab chris mahon worldbuilding fantasy spells

Music is made of patterns and mathematics, and the same kinds of waves that describe sound can apply to light, energy, and matter (I dove into sound waves and quantum mechanics in this post). In my sketches, I started to see how a given spell could be expressed as a song as well as a mandala-like graphical representation. And if you look back to wizards like Vainamoinen, spell-songs are exactly what mages used to change the world around them. It’s a really cool piece of synchronicity, and it’s one of the fascinating coincidences that pops up when you delve into this kind of worldbuilding.

Metaphysics, Spell Maps, and the Universe

But when I looked closer at my sketches, another pattern started to appear. I started to see how a spell map could also be a reflection of the symmetry of the universe, in the same way that Buddhist and Hindu mandalas supposedly reflect the order of all creation. In fact, the structure of a spell map looks like a universe of sorts: it’s a miniature galaxy, with spiral arms containing dozens of individual ‘solar systems’ (symbol-rows grouped around the center of a shape) containing sometimes hundreds of individual ‘worlds’ (symbols) and comprising thousands of ‘people’ (individual strokes that make up the symbols).

In my conception of this magic system, this is where magic crosses over from being a computer program and reveals its ties directly to metaphysics. Like a fractal, the pattern of the whole universe is expressed in miniature in the spell map, because magic is essentially a way to change the universe. And in this system, the way to change reality is to build a microcosm of the universe and rewrite it by hand. In this way, a spell map could also act as a kind of divination or scrying tool, like the I-Ching (a book that fascinated Phillip K. Dick to no end), reflecting the conditions of the world rather than changing it.

mandala occult triangle lab spell maps


Great worldbuilding should work like an iceberg: 10% on the surface, 90% below the waterline. I think this is one of the reasons the worldbuilding in Dark Souls rakes in such unreal praise. There’s a sense that beneath the immediate information you’re given, there’s whole volumes of knowledge and secrets to learn and immerse yourself in. It’s the opposite reason people can’t get through Lord of the Rings or The Silmarillion. But whether you’re revealing all of it or letting the reader unravel how everything fits together, I think the best way to accomplish that feeling of a vast, immersive world is to actually build it behind the scenes. I spoke about this before, but the small details are crucial to making fantasy work, and this is especially true when it comes to magic.

So if you’re a fantasy writer building a world from the ground up, explore everything. Everything feeds into everything else, the world is a frightening and wonderful place, and when you dig deep enough, triangles lie at the heart of everything.

occult triangle lab mandala

Worldbuilding: Spell Maps and Magic Systems

Narcomancy: Morphine, Lucid Dreaming, and Binaural Beats


If Captain Jack has taught me anything, it’s that sometimes you’ve got to dream a little dream. He doesn’t have much advice about how to build a magic system around dreams, though. N.K. Jemisin already uses the term ‘narcomancy,’ meaning dream magic, in her Dreamblood series, but after sketching out the magic system for the new story I’m working on, I found my narcomancy resembled William Gibson’s Neuromancer more than Killing Moon.

In a similar way to Case in Neuromancer, the narcomancers in my story operate by immersing themselves in an alternate reality and working from the inside. The reality in this case isn’t a Matrix, but a dreamscape that stretches across the world, with dreams and dreamers showing up as brainwave patterns, tuned to certain frequencies like bands of radio stations, each frequency representing a different stage of sleep—alpha, theta, delta, or REM.

I got the idea of imaging brainwaves as radio bands from Kevin Mitnick’s memoir, Ghost in the Wires, which explains (sometimes tediously) how he and many other hackers started out as ham radio operators. There was one repeater frequency, 147.435, that they called “the animal house,” a channel that was open for anyone to scream into, spread rumors, or meet random people. I liked the idea of tuning a radio into a certain frequency and hearing people’s dreams from all over the world, sort of like John Cheever’s The Enormous Radio. The idea for a worldwide dreamscape also came partly from Serial Experiments Lain, which touched on the Schumann resonance as a means to create a worldwide consciousness using the Earth’s magnetic field, then merge reality and the Wired into one. These ideas are really interesting to me, partly because they straddle the line between real scientific phenomena and fantasy.

The dreamscape, as I’m imagining it, can be visualized as having several different bands, or layers, each one corresponding to a different sleep stage:

dreamscape diagram

Part of the job of the narcomancers in the story is to find “bands” of dreamers in delta sleep and begin trying to trigger them into moving into REM sleep, where they can start manipulating their dreams. REM stage sleep is also known as paradoxical sleep, because it closely resembles the waking state of brain activity. It’s strongly associated with vivid dreaming, and it’s usually in this stage that you have real trouble distinguishing reality from dreaming.

REM stage sleep is also when a sleeper’s eyes begin to move rapidly behind their lids, hence the name: Rapid Eye Movement (REM). Imagining someone’s eyes moving hyper-fast, as if trying to keep up with thousands of flashing images, made me think of the mentats in Dune, who have a similar association with eyes. Their blue-tinted mélange-addicted eyes signaled their superhuman ability to think and process facts like computers, and in a similar way, I imagined  a sleeping narcomancer attaining an almost superhuman level of consciousness during REM, allowing them to deal with huge amounts of sensory input and making them able to pull off a performances.

REM stage sleep, like every kind of sleep, comes in cycles, with the brain diving and rising through the different stages several times over the course of one night. As the night goes on, REM stages become more frequent:


This brought me to another idea: sort of like a bank heist, what if narcomancers could only operate during their REM sleep, in 40-50 minute periods? It would almost be like a high that would wear off in time, forcing them to operate quickly, get in, play their music, and get out before their REM abilities wore off.

But there would have to be another hurdle for narcomancers to help distinguish them from regular dreamers: lucid dreaming. When I dream, it usually feels like I’m in a trance, like I’m watching myself doing things from somewhere slightly removed from my body with no real conscious control (Fun fact: sleep paralysis, a possible side effect of being woken up from REM sleep, often causes this same feeling, called bodily dissociation, also known as ‘having an out-of-body experience’). How could narcomancers, and musician narcomancers, hope to operate something akin to a mental DJ set when their mind isn’t working at top capacity? The only way to attain that kind of conscious acuity would have to be through lucid dreaming, where one would be able to recognize that they’re dreaming, then think and act as if they were awake.

To answer the question of how to attain lucid dreaming, I turned to 1980’s drug culture. Since the story was originally inspired by the rave-like EDM concerts of bands like Daft Punk, I turned to one aspect of rave culture: party drugs. So I invented a liquid, opium-derived product with a lot of similarities to morphine, which is apropos since morphine derives its name from Morpheus, the god of dreams. It’s also the kick-ass main character of Neil Gaiman’s Sandman series, but that’s another story entirely. Sezumi, this fictional drug, would have one new feature apart from morphine: it would allow lucid dreaming once it put someone to sleep.

But another aspect of narcomancy, one of the key elements of manipulating dreams, comes from a unique phenomenon that’s also connected to lucid dreaming: binaural tones. Caused by playing two high-frequency notes with slight difference in their frequencies, binaural tones are sine waves that cause the brainwaves of the listeners to begin to synch with the binaural frequencies, meaning that you can ‘tune’ your brainwaves to certain patterns, such as theta or delta rhythms. This would be tremendously useful for a narcomancer who has to move between different stages of sleep, but there’s another use for it that makes it the central skill of narcomancy when paired with lucid dreaming: synching your brain waves with the brain waves of dreamers, then manipulating them.

Consider it a very primitive form of hacking, to use the Neuromancer analogy again. While lucid and on your REM high (with a 40-minute window) you find a frequency band with many dreamers’ brain waves operating on that wavelength, then start using binaural beats to manipulate them into attaining REM stage, then fine-tune your brainwaves to match theirs. Once you’re on the same frequency, you’re the only lucid person around, while everyone else is operating on the subconscious level. From there, you can begin manipulate and shape the dreams into something like reality-bending art, using music as your tool.


Narcomancy: Morphine, Lucid Dreaming, and Binaural Beats

POETRY IN MOTION Part 1: Magic as Poetry

Before I talk to you about magic, I challenge you to write something in iambic pentameter. Better yet, write a sonnet. Learning the pattern of stressed, unstressed syllables makes you pay attention to the rhythm and emphasis in your voice and sentences, and the stitching and unstitching of lines to fit the syllable count makes you think of the most efficient, concise way to convey your point—what words are the best ones to express the sound of the sea? The challenge of creating rhymes also makes you stretch yourself and plan ahead—what word do you want to end the poem with?

Writing a poem forces you to think in a certain mode, one that pays attention to the micro scale of things: syllables, rhymes, words, sentences. But when the poem is finally written according to the form, you have to step back and see if all the technical tweaks and revisions add up to something that evokes a certain effect. This is the deus ex machina of poetry. All the syllables, words, lines, and rhymes add up to more than the sum of their parts: they tell a story, evoke a feeling, or paint a vivid picture in people’s minds just by being read. A great example is Dylan Thomas’ famous poem:

Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.

Though wise men at their end know dark is right,
Because their words had forked no lightning they
Do not go gentle into that good night.

Good men, the last wave by, crying how bright
Their frail deeds might have danced in a green bay,
Rage, rage against the dying of the light.

Wild men who caught and sang the sun in flight,
And learn, too late, they grieved it on its way,
Do not go gentle into that good night.

Grave men, near death, who see with blinding sight
Blind eyes could blaze like meteors and be gay,
Rage, rage against the dying of the light.

This is a villanelle, a poetic form that forces writers to repeat two lines in a refrain. In this case, the two lines are “Do not go gentle into that good night” and  “Rage, rage against the dying of the light”. The villanelle is associated with obsession because of the repetition inherent in it, as if the author is repeating those two lines to themselves, over and over in different configurations, with all the rhymes based around those refrains.

I think that’s fascinating—that a specific pattern of lines, syllables, and rhymes can be especially suited to evoke obsession. It makes me think of the yoik tradition of the Sami, the native people of northern Sweden and Norway. A yoik is a song, sometimes spontaneous, that uses a combination of words and notes to evoke a person, place, or thing. It’s not about something or someone, it’s their essence summoned to a given time or place for the duration of the yoik.

What if magic could be poetry? Not just in the spoken sense, but in the mathematical, metaphysical sense? What if its structure evoked its subject, like the villanelle or a yoik? What if art imitated life? What if there was no difference between art, magic, and living?


Building off my last post about the conversion of magical ‘true names’ to binary, magical ASCII format, and eventually spoken/written syllables, there’s another dimension of magical notation to explore: how magicians write their spells.

Magic, to me, would look like computer code when written out in symbols: each spell would have parameters, a specific range of targets, and “commands,” with universe acting as the computer. The actual language of this code would take…years to develop, like a new programming language. But I’ve come up with some groundwork for it, and that’s the important element.

For my magic system, I imagine having 40 discrete magical syllables that make up all words, including true names and the accompanying magical programming terms that would form the scaffolding for spells. Magicians would have to learn this language and how to write in it, similar to computer coding, but there are added dimensions to it, ones that turn magic from UNIX into a kind of metaphysical poetry.

Supposedly, when a sculptor begins chiseling a work out a marble block, the sculpture is already inside the block—they just need to ‘free’ it. When you write a poem, you can think of the same metaphor: you have a set number of syllables, lines, and rhymes, and your poem exists somewhere within those constraints—you just need to find the right words to free it. A contrast would be computer coding, where you start with a blank slate and have to build your own sets of rules in order to realize your goal. If the constraints of a poetic form creates one perfect path to the goal, computer coding is free-verse, with a thousand possible solutions, all with varying degrees of efficiency.

If magic was essentially computer code, you would start from scratch and run dozens of trial-and-error tests until you struck upon something that worked. You would have no clue as to what the final spell would look like, how it would be structured, or how it would work. Instead, I envision magic with tens of thousands of built-in patterns, which can be learned like the rules of a poem and solved like Sudoku puzzles, with perfect solutions that can be derived in a similar way someone goes about writing a sonnet. Instead of magicians trying to impose order on a blank slate of a world, they need to learn the patterns that are woven into every aspect of it.

To be continued in Part 2.

POETRY IN MOTION Part 1: Magic as Poetry