Neural Field Visualisation · WebGL · 2026
A scrollytelling WebGL experience that runs the Wilson-Cowan neural field equations in real time on a GPU. An artistic interpretation of the mathematical transformation DMT may apply to the primary visual cortex.
Launch experience →Many existing DMT visualisations make the same mistake: they add exotic content to a blank canvas. Fractal renders, VJ loops, AI-generated imagery. All of them attempt to depict the experience through novelty. This does the opposite.
plan.form takes an unremarkable photograph and asks: what if the pattern was already there, implicit in the spatial statistics of the image? As a single parameter rises from 0 to 1, the visual cortex's own lateral connectivity amplifies until it overcomes the external signal and begins generating structure spontaneously.
The geometry is not drawn. It is the stable solution to a differential equation, the same equation that governs V1 lateral connectivity in every human brain. What the mathematics produces is structure. Turning that structure into an image took a great many decisions that are not in the mathematics, and those are listed openly further down.
This is an artistic interpretation built on scientific models, not a scientific demonstration. The neuroscience grounding the simulation is well-established; the claim that this is what the DMT experience is is not. That gap is intentional, and worth keeping in mind.
Scroll position maps directly to shader uniforms. There is no timeline, no animation loop driving the narrative, only the reader's own pace through the mathematics.
The act boundaries are not free dramaturgy. They follow the six-level phenomenology that recurs across the trip report corpus, as collected and ordered by Gomez-Emilsson (2016, non-peer-reviewed): Threshold, Chrysanthemum, Magic Eye, Waiting Room, Breakthrough, Amnesia. Where this piece stops, and why, is set out at the end of the section.
One word has to be kept apart from itself. Threshold in those reports is the first level: a shift in ambience and a sharpening of the senses, with no geometry at all. Threshold crossing in a neural field means the bifurcation point. They are one level apart, and act III is the second of them.
The photograph is rendered as a luminance-displaced 3D surface. Each of the 197,000 vertices is pushed outward in proportion to local brightness. Brighter regions protrude, darker regions recede. Mouse movement drives camera parallax. V1 receives this signal. Its lateral connectivity is active but stable, patterns suppressed by the dominance of external input.
The first reported level, and the quietest one. Colours lift, local contrast sharpens, and the scene reads as though an intervening medium had been removed. No geometry, no motion, only more of what is already in the frame. α is still zero and the field is idle: what happens here is a colour grade and a four-tap local contrast lift applied to the photograph. It is in the piece because the corpus puts it first.
The Wilson-Cowan field comes up alongside the image: two coupled populations, excitatory and inhibitory, 8 integration steps per rendered frame on a 512² grid. Lateral excitatory coupling wEE then crosses its critical value and the homogeneous steady state loses stability through a Turing instability. Patterns form spontaneously, not from noise but from the image's own fine structure, which seeds the planform nodes at texture boundaries.
The field self-organises into the planform Bressloff et al. (2001) predict for V1 under elevated cortical excitability: the gain increase hallucinogens are thought to induce via 5HT2A-mediated action on V1. Flat, apersonal, no figures yet. The reports describe this level as symmetrifying whatever patterned surface is looked at, which is exactly the split here: the kernel sets the symmetry class and the spacing, the photograph sets where the nodes land. Terence McKenna's name for it is the one that stuck.
The texture is read as an autostereogram. Dark recedes, bright advances, and a surface becomes a volume. The height map is the field itself: nodes rise, anti-nodes sink, the mid-range flattens into a floor, and what lifts out of the wall carries the planform's symmetry because it is made of the planform. In the reports the fold comes from recognition, and whatever is recognised takes on the excess curvature. That half is not in the code. It is happening in whoever is watching.
The Poincaré disk transform reaches full strength and z → log(z) maps the visual field to cortical coordinates. The room closes. Bilateral, nodal, axially organised structure is what face-selective cortex responds to, which is a claim about the person looking at the screen and not about the field behind it. In the reports the entities are a gradient across four levels; this act shows one point on it.
Plasma concentration peaks two to three minutes after injection and the effects decay across the following quarter hour (Timmermann et al., 2019). Whole-brain models fit the bifurcation parameter as a gamma function, fast rise and slow fall (Piccinini et al., 2025). So α falls, the curvature relaxes, the cortical map unwinds and the photograph comes back. It is the same photograph. Earlier versions held the parameter at maximum to the end, which matched neither the pharmacokinetics nor the reports, both of which are dominated by the way back.
Levels five and six of that phenomenology, Breakthrough and Amnesia, are deliberately not attempted. The reason is structural rather than a shortage of effort. The source defines a breakthrough as a topological change of the world-sheet: the connectivity of represented space changes, loops open between points that had none. Everything in this piece is a change of curvature applied to a depth-mapped surface, and a depth-mapped surface cannot change its own topology. Amnesia is by definition not representable.
So the work covers levels one to four of six and stops there. Naming the boundary is what makes the rest of it worth reading.
The simulation runs two coupled ordinary differential equations per spatial point on a 512 × 512 grid, updated 8 times per rendered frame via WebGL2 ping-pong render targets:
τ_E · ∂E/∂t = −E + σ( w_EE · K_exc⊛E − w_inh · K_inh⊛E − w_EI · I + I_ext ) τ_I · ∂I/∂t = −I + σ( w_IE · E − w_II · I ) I_ext = luminance · (1−α) · 0.45 + edgeEnergy · 0.10 σ(x) = 1 / (1 + exp(−5 · (x − 0.28))) [sigmoid activation] ⊛ = spatial convolution with lateral connectivity kernel
Both kernels sample the excitatory field: Kexc over a short radius, Kinh over a long one. Their difference is the Mexican hat. Note that the second term in Iext does not scale with α, which is why the pattern stays anchored to the image at every value of the parameter.
The spatial convolution uses two ring samplers in GLSL: a 12-point ring (30° spacing, 6-fold symmetry) at radius 6 px for short-range excitation, and a 16-point ring at radius 20 px for long-range inhibition. Their difference approximates the Mexican-hat lateral connectivity kernel: the anatomical reality that excitatory neurons form local clusters while inhibitory interneurons project further. The 12-point ring's 6-fold symmetry is deliberate: an 8-point ring would introduce 4-fold bias and spuriously favour square-lattice planforms over the hexagonal class V1 prefers.
Strictly speaking, this is a reduced formulation: the inhibitory equation uses only local E (no spatial kernel on the E → I coupling), placing the system between the full Wilson-Cowan model and the Amari (1977) single- population neural field. The simplification is standard, preserves the Turing-instability behaviour, and keeps the GPU cost low enough for real-time integration at 60 fps.
The parameter α represents the DMT effect. As α rises from 0 to 1, two things happen simultaneously: external input is suppressed by factor (1−α), and lateral excitatory coupling wEE rises from 0.45 to 1.75. Below α ≈ 0.42, every spatial point converges to the same resting activity (E* ≈ 0.35). Above this threshold, the homogeneous state loses stability.
This is a Turing instability (Turing, 1952). The critical wavevector k*, the spatial frequency that first goes unstable, is determined by the ratio of excitatory to inhibitory kernel radii. For rexc = 6 px and rinh = 20 px, a rule-of-thumb estimate over those radii puts the characteristic wavelength near 52 px; the true value for a 12- and 16-tap ring difference deviates from this. The same mathematics that spaces the spots on a leopard's coat spaces the nodes of the DMT pattern.
The external input Iext includes a persistent high-frequency edge signal derived from the image texture. This seeds planform nodes at image texture boundaries, ensuring the pattern that emerges is topographically anchored to the input, not arbitrary.
In 1928, psychologist Heinrich Klüver systematically documented the geometric patterns that appear universally across mescaline experiences, sensory deprivation, hypnagogia, and migraine aura. He identified four fundamental classes: gratings and lattices, cobwebs, tunnels and funnels, and spirals. He called these form constants and proposed they reflect the intrinsic organisation of the visual system.
Fifty years later, Ermentrout and Cowan (1979) provided the mathematical explanation. They showed that the visual cortex, modelled as a neural field with lateral connectivity, undergoes symmetry-breaking instabilities that produce exactly these four pattern classes. The patterns are not content imposed on the cortex. They are the cortex's own structural resonances, made visible when external suppression is removed.
Bressloff et al. (2001) extended this analysis with full consideration of V1's functional architecture (orientation preference columns, ocular dominance, the anisotropy of long-range horizontal connections) and showed that the symmetry group of V1 connectivity constrains the emergent planforms to a small set of geometric forms. These correspond precisely to Klüver's form constants. The hexagonal planform, which this simulation produces, is predicted for uniform, isotropic inputs under elevated cortical excitability: the gain increase classical hallucinogens are thought to induce via 5HT2A-mediated action on V1.
That same paper draws a line this simulation sits on the wrong side of, and it is worth stating plainly. The field here is a single-population reduction with an isotropic Mexican-hat kernel and no orientation dimension, which places it in the Ermentrout-Cowan class rather than the orientation-tuned one. Bressloff et al. are explicit about what that class can and cannot do: "The absence of orientation representation in the Ermentrout-Cowan model means that a number of the form constants cannot be generated by the model, including lattice tunnels, honeycombs and certain chequer-boards, and cobwebs."
What this class does generate is contrasting regions of light and dark, which under the inverse retino-cortical map give tunnels, funnels and spirals. Honeycombs and lattices need oriented contours, and oriented contours need a dimension this field does not have. The honeycomb quality on screen, the part that looks most like the reports, comes from the photograph's texture and from the composition. It is not a product of the model class. Separating the two is the whole point of the piece, and this is the sharpest place where they come apart.
The same limit shows up as a symmetry count. An isotropic kernel on a doubly periodic lattice supports three lattice types, rhombic, square and hexagonal, which in wallpaper terms is at most p2mm, p4m and p6m. Three of the seventeen plane symmetry groups. Reports of psychedelic visuals claim all seventeen. That gap is not a rendering limitation that better shaders would close; it is a property of the model. The n-fold selector in the laboratory reaches past it by injecting an angular modulation by hand, which is listed below with the other imposed effects.
The visual field does not map linearly to V1 surface area. The central 10° of vision maps to approximately half of V1's surface, despite covering only a small fraction of the total visual field (Horton & Hoyt, 1991). This magnification follows a logarithmic relationship, the retino-cortical transform, described by the complex logarithm. The transform implemented here reproduces the logarithmic form of that magnification qualitatively; its constants are chosen for framing, not fitted to the published magnification factor:
w = log(z) where z = x + iy is position in the visual field In polar coordinates (r, θ): cortical x = log(r) cortical y = θ Implemented in GLSL: cx = (log(r) + 3.22) / 3.57 cy = atan(y, x) / (2π) + 0.5
Radial patterns in visual space become vertical stripes in cortical coordinates. Concentric rings become horizontal stripes. The planform, which lives in cortical coordinates, appears as a radially symmetric mandala when mapped back through the inverse transform. The doubled, figure-like forms of the final act do not come from a symmetry operation. They come from the angular wrap of the log-polar map combined with the imposed displacement described under Honest accounting.
Andres Gomez-Emilsson (2016) of the Qualia Research Institute proposed that DMT transforms the underlying geometry of phenomenal space from Euclidean to hyperbolic. In hyperbolic space, the circumference of a circle grows exponentially with radius rather than linearly, providing exponentially more "room" per unit radius. This accommodates the information overload of DMT-amplified lateral connectivity, and may explain the reported quality of "more real than real": more information is encoded per perceived unit of space than is possible in Euclidean geometry. Note: the QRI essay is a speculative philosophical proposal, not a peer-reviewed publication. It is used here as conceptual inspiration for the Poincaré disk transform, not as empirical evidence.
The Poincaré disk model maps the entire infinite hyperbolic plane into a unit disc. Implemented here via:
r_texture = tanh( atanh(r) / (1 + t · 1.2) ) where r = normalised screen radius, t = curvature parameter [0,1]
This produces the disc-shaped mandala characteristic of peak psychedelic visual geometry. The centre expands without apparent limit; the boundary recedes forever.
One qualification on that transform, because the source is more specific than the implementation. In the QRI account the curvature is a local quantity driven by attention: it accumulates where measurements have already been made, and only jumps to the whole space when a surface can no longer hold it. Here it is a single global parameter applied to the entire frame at once, centred on the middle of the image and unrelated to where the field is active. The name of the mechanism is borrowed correctly; the operator is not the one described. It is listed with the imposed effects below.
The local half of that idea is what act V implements. The field's deviation from rest is read as a height map rather than as a brightness modulation: nodes advance, anti-nodes recede, and the mid-range holds still as a floor, so the plane acquires volume and forms stand out of it. Those forms are patterned with the planform because they are made of it. The height map is field-derived; the single key light and rim term that make it read as relief are not, and are listed below. An earlier version produced this effect from the photograph's own luminance in the final act, which gave the same silhouette at every parameter value and put a photographic decision where a reading of the field belongs.
The fusiform face area (Kanwisher et al., 1997) responds to the structural features of a face (bilateral symmetry, nodal eye positions, axial organisation) independent of whether the input is literally a face. That is a claim about the person looking at the screen, not about the simulation behind it. This may be a neural correlate of the figure-like forms reported at the threshold of the experience: pattern completion operating on a supercritical neural field. Whether that accounts for the full phenomenology, meaning the agency, the narrative and the emotional weight of entity encounters, is an open question the model does not resolve.
The neural field is real: two coupled populations, integrated on the GPU, with no scripted outcome. Everything that follows the field is a design decision. Separating the two matters more than either does alone, so here is the full list.
The symmetry class and the characteristic wavelength of the planform follow from the connectivity kernel and from nothing else. The bifurcation is a real loss of stability: below the threshold the homogeneous state is an attractor, above it the patterned state is. The activation front is not a visual overlay. It gates the simulation itself, so cortex outside the front stays sub-bifurcation until the front arrives.
The shape of the world-sheet in act V as well. The height at every vertex is the local deviation of the excitatory population from its resting state, split asymmetrically so nodes advance and anti-nodes recede. Where the forms stand and what they look like is decided by the simulation, not chosen.
Where the nodes land. A persistent high-frequency term derived from the input texture enters the external drive and does not fade as the parameter rises, so the pattern stays topographically anchored to the photograph throughout. The kernel decides what class of pattern forms; the image decides where it forms. An earlier version of this text claimed the planform was independent of the image beneath it. That was wrong in the second half.
The laboratory offers two groups of input texture, and the difference between them decides what the simulation is being tested on.
A control input carries no symmetry: broadband, isotropic, no privileged orientation and no privileged spatial frequency. Pink noise, band-limited noise, woodchip wallpaper, or a photograph. There is nothing in it for a planform to be copied from, so whatever symmetry appears came from the connectivity kernel. This is the case Ermentrout-Cowan and Bressloff actually describe, and it is the default.
A resonance input already carries a form constant, and the rings texture carries it in cortical coordinates, which is to say it is already the pattern the kernel is supposed to produce. Loading one of those and watching a planform appear proves nothing about emergence. It tests something narrower and still worth seeing: whether the field's characteristic wavelength matches the input's spatial frequency. If it matches, the pattern locks and sharpens. If it does not, the field overrides the input and imposes its own spacing.
Both groups are on the tile strip and both are labelled. Switching between them is the quickest way to see which parts of the image belong to the mathematics and which parts were handed to it.
A second control sets the viewing distance. Nothing moves and no camera changes: the texture is regenerated with proportionally finer features, which is what stepping back from a wall does to the image landing on a retina. Tiling the texture would have been cheaper and was rejected, because every tile boundary is a straight edge, edges enter the external drive, and a tiled input prints its own grid into the pattern.
There are two steps, and that is the whole useful range, because the second one crosses something. At distance 1 the input's features sit above the field's characteristic wavelength and the image decides where the nodes go. At distance 2 they fall to it and past it, the field stops locking to the input and begins imposing its own spacing. Structures appear that the input never contained: run the oriented stripes at distance 2 and hold past the peak, and symmetries emerge there that distance 1 does not produce at any parameter value.
That is the clearest single view in the piece of how much of the geometry belongs to the input and how much to the kernel. A third step would only push further into the same regime, where everything below the field's wavelength looks alike to the field and the images converge.
The face-like forms of the final act are a statement about the viewer, not about the simulation. Face-selective cortex responding to bilateral, nodal, axially organised structure is a claim about a human looking at a screen. The screen is not doing it. Whether the same account extends to entity encounters under DMT is an open question, and this piece raises it rather than answering it.
It does not claim to produce the pattern class it most resembles. The field belongs to the model class Bressloff et al. show cannot generate honeycombs, lattices or cobwebs, and it spans three of the seventeen plane symmetry groups where the reports claim all seventeen. The lattice quality on screen comes from the photograph and the composition.
It does not claim to cover the experience. Of the six levels the reports describe, this covers four and stops before Breakthrough, which is a topological change rather than a change of curvature, and before Amnesia, which is not representable at all.
It does not model recognition. Act V reads the field as depth, but the source attributes the fold to recognition: whatever is recognised takes on the excess curvature. Nothing in the code recognises anything. That half of the mechanism is supplied by the person watching, which is either the weakest part of the piece or the most interesting one.
The following sources shaped the conceptual framing and visual language of this project. They are listed separately not as a dismissal of their intellectual value, but to distinguish their epistemic register from the peer-reviewed literature above.
McKenna's ethnobotanical and cultural work operates in a tradition of experiential inquiry and synthesis that sits outside, but not beneath, academic convention.
Gomez-Emilsson's two essays represent serious independent theoretical work in the phenomenology of altered states, produced within the Qualia Research Institute's research programme, and engage directly with mathematical and geometric frameworks. Both are load-bearing here: the six-level sequence that sets the act boundaries comes from one, and the two operators running as post-effects come from the other.
Four works shaped the visual language and technical approach of this project. Each contributed something that could not have been derived from the scientific literature alone.
| Work | Creator | Contribution |
|---|---|---|
| field-transformations |
HAL09999 danslesnuages.xyz fxhash profile |
Fragment shader wave superposition architecture. Binaural audio synchronised to field frequency. Contemplative pacing: a click as ritual, not control. The restraint that separates scientific visualisation from generative spectacle. |
| Pressure Radial Flow |
Justin Shrake (j2rgb) j2rgb.com jshrake.com github.com/jshrake |
Post-processing stack architecture: bloom → radial chromatic aberration → ACES filmic tonemapping. Ping-pong MRT state texture structure for E/I fields. The plasma volume pass (screen-space Gaussian blur of the sim texture, depth-masked to dark scene regions) extends this pipeline with a bioluminescent interior glow. |
|
study-particle-landscape MIT licensed |
Taylor (taylorallenux) github.com/taylorallenux |
Neural field as heightmap driving vertex displacement. Travelling wave activation front as reveal mechanism. Height-based colouring with threshold zone interpolation. |
| jellyfish.html |
Original concept: yuruyurau x.com/yuruyurau PWA implementation: itd286904 |
Lobe-count parameter as planform mode selector (n-fold rotational symmetry). Nested sin distortion as nonlinear activation function. Almost-periodic temporal behaviour that prevents the pattern from ever exactly repeating. |
All four works are credited as influences on the visual language and technical approach, not as direct code imports. study-particle-landscape is published under the MIT license; the other three works do not carry an explicit source-code license and are credited here under fair-use attribution for artistic influence.
| Project | Role |
|---|---|
| Three.js | 3D rendering, WebGL2 abstraction, GPUComputationRenderer ping-pong for the neural field simulation. |
| GSAP / ScrollTrigger | Scroll-driven uniform animation. ScrollTrigger maps document scroll progress to shader parameters without any per-frame JS overhead. |
| Vite |
Build tooling. Raw GLSL imported as strings via the ?raw
suffix. Zero-config static output deployable on any server.
|
works as a systems engineer at a managed service provider, where most of his professional time goes to IT infrastructure, containers, automation and the integration work that keeps businesses running without announcing itself. The remainder goes in part toward reading: Hofstadter on strange loops, Jaynes on the origins of consciousness, Tegmark on the mathematical structure of physical reality, Rovelli, Dennett, Penrose. The kind of accumulation that builds slowly and occasionally produces unexpected outputs.
This project is one of them. It began with a narrow question: why do geometric visual constants recur so precisely across different altered states, and why do existing visualisations consistently fail to honour the precision the underlying mathematics actually offers? The implementation, a GPU-resident Wilson-Cowan simulation running in a browser driven by scroll position, required considerably more GLSL than originally seemed reasonable. The mathematical foundations, at least, are well-established. What they fully explain is not.
pk [at] sponde [dot] de
github.com/Kracht
The full source code for this project is available on GitHub under the
MIT licence.
github.com/Kracht/plan.form