Visual cortex and form constants
Use this page to compare animated V1 planforms with classic form-constant shapes: tunnels, spirals, cobwebs, lattices, and honeycombs. The Bressloff visual-cortex model gives a concrete way to ask how simple activity patterns in primary visual cortex could appear as tunnels, spirals, cobwebs, lattices, and honeycombs after the retino-cortical map. The useful test is modest and visual: choose a cortical planform, transform it through the visual-field map, and see whether the named Kluver-like form appears (Bressloff et al., 2002).
Public status
This page uses generated model images unless a caption explicitly says otherwise. Source-paper figures are named as calibration targets and references, not reproduced assets. No source-paper scans or crops are hosted here unless a license or permission statement appears in the caption. Full PDFs, page images, and source-figure crops are not published from this page.
Rule et al. 2011 figures may be reused from PLOS Computational Biology under Creative Commons Attribution terms with attribution and change notes. Bressloff/Royal Society, Bressloff/Neural Computation, Ermentrout and Cowan/Springer, and IOP review figures require separate license verification or permission before direct reproduction (PLOS license policy; Royal Society permissions; MIT Press permissions; Springer Nature permissions; IOP permissions FAQ).
The animations test whether V1 planforms can produce recognizable geometric forms after visual-field mapping. They do not predict individual hallucinations, psychedelic experience, clinical outcomes, or safe flicker exposure.
These animations are explanatory model loops, not flicker stimuli or safety-cleared visual stimulation protocols.
Limits
If V1 is treated as a two-dimensional cortical sheet with orientation structure, then symmetry-breaking activity patterns can become recognizable geometric visual forms after projection into retinal coordinates. That is a strong mechanistic sketch for form constants, while psychedelic imagery, visual meaning, and calibrated strobe-frequency prediction require additional models and evidence (Ermentrout and Cowan, 1979; Bressloff et al., 2002).
Flicker can induce geometric visual hallucinations, and newer work studies those reports with richer phenomenological instruments. A V1 planform model starts upstream of exact frequency claims: it first makes cortical pattern families tunable and visible. A later layer can try to connect input frequency, neural drive, participant state, and report structure (Rule et al., 2011; Hewitt et al., 2025).
Animated figure presets
These animations are exported from the Rust V1 planform renderer, then served as static WebP loops. They drift slowly to reveal structure rather than produce flicker. If reduced motion is enabled, the browser receives static PNG poster frames instead.
Source-target registry
Each row links the source figure reference and places the current generated implementation beside the formula path used in the Rust renderer. The hosted images are generated assets from this repository; source-paper scans remain references until reuse permission or an open license is clear. For a non-journal visual explainer of this model lineage, see CountYourCulture's Bressloff notebook. Rights for original journal figures remain separate; this page uses generated images unless permission or an open license is stated.
The interactive implementation now carries 24 named Bressloff presets: Figure 16/17 stability examples, Figure 29/30 non-contoured single-map planforms, Figure 31-36 double-map contour planforms including roll subpanels, and 2002 Figure 5-7 convenience targets (Bressloff et al., 2001; Bressloff et al., 2002; implementation repository). The generated report separates rendered-target checks from amplitude-branch diagnostics, so a square/cobweb image can be marked as visually rendered while its current branch selector still prefers the roll family.
Square/cobweb even planform in the detailed Bressloff et al. Royal Society treatment.
Source figure reference Open visual comparison
fig31_square_even presetTwo orthogonal cortical modes are rendered through the double map. The target planform renders as cobweb/square; the same-lattice branch readout currently selects the roll/spiral branch.
Odd square/cobweb variant for checking parity-dependent contour structure.
Source figure reference Open visual comparison
fig32_square_odd presetThe odd branch uses the same square lattice target with the odd orientation eigenfunction. The rendered family matches the target; the local stability readout again falls to roll/spiral.
Rhombic even planform, used here as the cleanest current same-family calibration case.
Source figure reference Open visual comparison
fig33_rhombic_even presetThe rendered planform, family check, and same-lattice branch selector currently agree. This is the baseline for the later figure-by-figure geometry calibration.
Hexagonal even phase variant. This row is the current phase-selection test for the quadratic amplitude term.
Source figure reference Open visual comparison
fig35_hex_even presetThe renderer draws the requested hex-pi variant. The same-lattice branch selector chooses the honeycomb phase partner under the current quadratic-term sign convention.
Interactive implementation
The animations come from a Rust V1 planform renderer with kernel parameters, an even/odd stability scan, perturbative orientation eigenfunctions, branch selection, and a retino-cortical viewer. Those controls make the model tunable enough to compare against the paper figures instead of treating each image as a fixed illustration.
The MIT-licensed implementation is MIT licensed and credits the public karacsm/V1-sim notebook lineage. Brain Candy is relevant only as adjacent state-shift context; the implementation itself focuses on Bressloff's model equations. The current calibration layer exposes named source-target presets, orientation-channel exports, and side-by-side checks between target planforms, contour mode, same-lattice branch selection, stability diagnostics, and generated output.
Implementation roadmap
The Bressloff papers now map to a public source-target registry and calibration report. The next fidelity layer is narrower: measure how well generated images match the source figures, fit phase and threshold conventions, digitize stability curves, and resolve the odd-hexagonal branch cases where higher-order terms matter (future implementation plan).
That distinction matters for later flicker work. Rule, Stoffregen, and Ermentrout's flicker-induced phosphene model belongs beside this V1 planform lab, but it should enter as a separate scalar excitatory/inhibitory model family rather than being folded into Bressloff's orientation-hypercolumn presets.
After Rule
Later neural-field work extends the classic form-constant lineage from spontaneous planforms and diffuse flicker toward driven systems. Nicks, Cocks, Avitabile, Johnston, and Coombes model Billock-Tsou-style orthogonal responses using spatial forcing and a 2:1 resonance (Nicks et al., 2021). Tamekue, Prandi, and Chitour treat MacKay-style effects as localized input-output problems in an Amari neural field (Tamekue et al., 2024). Bolelli and Prandi add time-periodic localized inputs and relate model afterimage contour width to flicker frequency and inhibition strength (Bolelli and Prandi, 2025).
These papers do not make the simulator a perception predictor. They show how the model family has moved from spontaneous forms toward stimulus-driven fields.
Frequency and input parameters are model variables, not safe exposure recommendations or promises about what an individual viewer will see.
The deep dive carries the full taxonomy, rights ledger, and extension notes.
The source papers name different author-side workflows: XPPAUT/AUTO, MATLAB, Julia, Mathematica, PETSc/Trilinos, and BifurcationKit appear in different parts of the lineage. Mesmer Prism records that methods context while keeping its own outputs generated and explicitly labeled.
The methods note separates named source software from the Rust diagnostics shown here.
Driven diagnostics
The public simulator now exposes source-safe generated reports for localized MacKay input, localized time-periodic input, and Nicks-style orthogonal response. Bolelli now includes an accepted source-side pole-width convention, generated decay-width fit diagnostics, and Figure 5 source-equation curve samples without source-panel calibration, while Nicks includes Appendix-B kernel-derived coefficient diagnostics, source-equation Figure 8 boundary residual checks, and a source-derived acceptance policy. These remain diagnostic outputs and compact numeric summaries, not copied paper figures and not calibrated perceptual predictions.
Reading the animations
A stripe in cortical coordinates can become a ring, a ray, or a spiral in visual-field coordinates because the V1 map uses log-polar structure rather than a rectangular image copy. Near the center of gaze, retinal eccentricity and polar angle are expanded into a log-polar cortical sheet. The same wave family can therefore look qualitatively different after remapping.
The short line overlays mark local dominant orientation channels: orientation hypotheses rather than separate moving objects. They are a compact way to show how an orientation-resolved model can turn scalar activity into contoured hallucination sketches, which is central to the later Bressloff account.
A simulator is useful here when it lets the model fail in public. If the equations cannot generate the named family under any plausible parameter setting, that is informative. If a small parameter shift moves the model from cobweb to rhombic to honeycomb, that is also informative. The point is to put the mathematical description close enough to the image that the comparison becomes checkable.
References