10 engines · 7 hypotheses · nulls
Some answers
are no.
A working physics bench for testing whether biological nanostructures might resonate—and for keeping the failed hypotheses visible.
H2, H6 undecidedH7 p=0.183active ring costs 40× a neuron's budget
Seven hypotheses, one browser
Start inside the cell: inside every one of your cells are tiny hollow tubes — microtubules — that form part of the cell's scaffolding. A handful of physicists have wondered whether these tubes might “ring” like microscopic antennas at particular frequencies. A few have wondered whether that might have something to do with how the brain works. This simulator tests seven specific versions of that idea with real physics, and reports the ones that failed. One came back statistically insignificant. A plain regular structure outperformed the fancy “fractal” one. Keeping the tubes actively ringing would cost a neuron roughly 16× its entire energy budget. It's a tool for sharpening the question, not a claim that the answer is yes.
What the page runs
- An exploratory computational tool for visualizing and testing hypotheses about microtubule resonance phenomena
- 10 real physics engines: RK4 integration, Monte Carlo sampling, Berry phase computation, stochastic resonance analysis, energy budget calculation
- A human–AI collaboration
- An attempt to sharpen questions, not to prove a predetermined conclusion
Where the claim stops
- Peer-reviewed research
- A claim that these computational results are experimentally validated
- A replacement for laboratory measurement or direct empirical observation
- An endorsement or refutation of any particular theory of consciousness
Why This Exists
In 2020 and 2022, Anirban Bandyopadhyay and colleagues published findings reporting fractal electromagnetic resonance in single microtubule nanowires. The reported pattern is a self-similar "triplet of triplet" that repeats across four frequency decades (Hz, kHz, MHz, GHz). They also reported that cytoskeletal filaments fire ~250μs before the membrane ionic spike — challenging the classical Hodgkin-Huxley model of neural signaling.
These are extraordinary claims. This simulator models them numerically to see which parts hold up.
This simulator was built to ask: Are these patterns mathematically plausible? Are they internally consistent? Could simpler structures produce the same effects? Not to prove or disprove, but to sharpen the questions that matter before (or alongside) expensive laboratory experiments.
What the Simulator Does
The simulator has five interactive panels and two operating modes. In Visual mode, it provides intuitive animated illustrations of the phenomena. In Computed mode, it runs real numerical physics engines and displays quantitative results.
Fractal Resonance Spectrum
The triplet-of-triplet pattern across Hz, kHz, MHz, and GHz scales. Click any peak to zoom into its fractal sub-structure.
Microtubule Cross-Section
13-protofilament chiral cylinder with resonance mode visualization. Sweep driving frequency to find resonances.
Temporal Cascade
Filament-first firing sequence showing the ~250μs lead time over the membrane ionic spike.
Holographic Projection
Optical vortex ring visualization of angular momentum states emitted by the internal clock assembly.
Hypothesis Lab
7 testable hypotheses with computational engines, revised verdicts, and 3 meta-analysis tools that interrogate the simulator itself.
Key Findings
Each hypothesis was tested computationally and assigned a verdict using a revised taxonomy that distinguishes between independent evidence, model self-consistency, and unvalidated claims.
| Hypothesis | Verdict | Summary | |
|---|---|---|---|
| H1 | Fractal Coherent Amplification | Plausible | The 36 fractal modes sum coherently to 17.7 vs random ~5.3. A regular lattice reaches 22.9. |
| H2 | Chirality Creates Triplets | Inconclusive | With every mode counted, the twisted tube does show triplet clusters, but no more than random splittings of the same size produce, and the verdict flips with small pitch and cutoff changes. The test cannot credit the triplets to chirality. |
| H3 | Boundary Dominates Bulk | Consistent | Sub-linear length scaling confirmed, but this is tautological — the model is confirming its own boundary assumptions. |
| H4 | Filament-First Temporal Ordering | Consistent | Fast oscillator leads slow oscillator as expected. Also tautological — built into the coupled oscillator structure. |
| H5 | Pitch Angle Optimality | Inconclusive | Peak at 4°, 8° from the actual 12° pitch, and the position depends on the αcritical parameter. Weakest robustness (55%). |
| H6 | Thermal Noise as Fuel | Inconclusive | A fair test with controls: driven slowly, the model shows stochastic resonance right where Kramers theory predicts (D = 0.40 vs 0.45). At its own drive no frequency met the criterion of a peak at least 3× a run with no signal. Not demonstrated. |
| H7 | Scale Invariance Predicts Schumann | Unvalidated | 4/5 Schumann harmonics matched, but Monte Carlo null test gives p=0.183. Not statistically significant. |
Meta-Analysis
What This Means
The fractal resonance pattern described by Bandyopadhyay is mathematically real but not uniquely special. Simpler ordered structures (like a regular lattice) can produce equal or greater coherent amplification. The specific triplet-of-triplet arrangement is not required: a plain regular lattice scores 22.9 against the fractal's 17.7.
Stochastic resonance (H6), the effect where a specific amount of noise makes a weak signal easier to detect, is not demonstrated at this model's drive frequency. We checked the test can see it: drive the same double well a hundred times more slowly and the textbook peak appears where Kramers' escape-rate theory puts it. At the model's own drive, from very little noise to a great deal, no frequency met the test's criterion of a peak at least three times a run with no signal at all.
The energy budget analysis provides a hard constraint: active MHz oscillation in microtubules is energetically implausible (requiring ~40x a neuron's total power budget). Any valid mechanism must be passive. Whether thermal noise could drive it is a rate question (attempt frequency and barrier) the model does not answer.
The Schumann resonance alignment (H7) — perhaps the most provocative claim — does not survive statistical scrutiny. Random fractal patterns match Schumann harmonics almost as well (p=0.183).
Simplified Hypothesis Guide
Each hypothesis explained without jargon, along with what we tested and what it means.
Fractal Coherent Amplification
PlausibleImagine 36 tuning forks. If they vibrate in random directions, they partly cancel out (like a crowd all talking at once — you get about 5x louder). If arranged in a specific pattern, they reinforce each other (like a choir singing in harmony — you get 36x louder). Our test found the fractal pattern does amplify the signal, but a simpler regular arrangement actually works slightly better. The nesting structure matters, but the specific fractal pattern is not uniquely optimal.
What we computed: Berry phase accumulation across 36 modes. Fractal = 17.7, regular lattice = 22.9, random average = 5.3, perfect alignment (all phases identical) = 36. Seed 20260906.
Chirality Creates Triplets
InconclusiveMicrotubules are twisted (chiral), like a spiral staircase. The question: does this twist create the triplet resonance pattern? We compared a twisted tube to a straight one, counting every resonance including both directions of rotation. The twist does produce groups of three, but random twists of the same size produce as many, and the answer changes with small parameter changes. So the test cannot say chirality creates the triplets, and it cannot rule it out either.
What we computed: Cylindrical standing wave modes (n from −12 to 12) with and without helical pitch, degenerate pairs counted once, against 100 random-splitting null draws and a 9-point pitch and cutoff grid.
Boundary Dominates Bulk
ConsistentDoes the amplification happen at the surface of the tube or throughout its interior? If it is a surface effect, making the tube longer should not help much (the surface-to-volume ratio decreases). Our model shows sub-linear scaling — consistent with a boundary effect. But this is the model confirming its own design, not independent evidence.
What we computed: Amplification factor vs. tube length. Scaling was sub-linear. Caveat: Tautological test — the boundary assumption was built in.
Filament-First Temporal Ordering
ConsistentClassical neuroscience says the membrane fires first, then the cytoskeleton responds. Bandyopadhyay's team measured the opposite: filaments fire 250 microseconds before the membrane. We modeled this as a fast oscillator (filament) coupled to a slow one (membrane). The fast one does lead — but that is what coupled oscillators do when one is faster. The model confirms its own structure, not the biological claim.
What we computed: RK4 integration of coupled ODEs. Fast oscillator phase-leads slow oscillator. Caveat: Expected from the math, not an independent prediction.
Pitch Angle Optimality
InconclusiveMicrotubules have a specific twist angle (~12 degrees). Is this angle special? We swept from 0 to 45 degrees and found a peak at 4 degrees, 8 degrees off the real pitch — and the peak position depends on a free parameter we can tune. With different parameter choices, the peak moves. This is the least robust result (55% stability under perturbation).
What we computed: Berry phase resonance condition and coupling efficiency vs. pitch angle from 0° to 45°. Peak at 4.0° (8° from the 12° pitch), sensitive to αcritical = 15°.
Thermal Noise as Fuel
InconclusiveUsually, noise destroys signals. But in certain nonlinear systems, a specific amount of noise makes the signal stronger — stochastic resonance. It happens when random hops between two states line up with the signal's rhythm. To test fairly, we first drove the model slowly and confirmed the effect appears, at the noise level physics predicts. Then we tried the model's own rhythm across a wide range of noise, next to a run with no signal at all: no frequency met the criterion of a clear peak at least three times that baseline, so the effect isn't demonstrated there. The earlier “nine-fold improvement” was a measurement artifact.
What we computed: Two-state (well-to-well) coherent power ratio vs. noise for a slow control drive (f = 0.01) and each native drive (0.7, 1.0, 1.4) over D = 0.2–7.5, plus a no-signal run as the baseline; 40 trials per point; control peak compared with the Kramers matching prediction.
Scale Invariance Predicts Schumann
UnvalidatedIf the fractal pattern extends to all scales, it should predict Earth's Schumann resonances (electromagnetic standing waves in the atmosphere at 7.83 Hz, 14.3 Hz, etc.). Our extrapolation matched 4 out of 5 harmonics. Sounds impressive — until we ran 10,000 random fractal patterns and found that 18.3% of them match just as well. This is not statistically significant (p=0.183). The apparent alignment may be coincidence.
What we computed: 10,000 Monte Carlo trials with random triplet patterns. Observed 4/5 matches vs. random mean of 2.58±1.02 matches. p=0.183.
Credits & References
This simulator was built with Claude agents (Anthropic), used both to develop the code and to help frame, test, and interpret the computational results.
Primary Source Material
- Bandyopadhyay, A. et al. "Fractal, Scale Free Electromagnetic Resonance of a Single Brain Extracted Microtubule Nanowire, a Single Tubulin Protein, and a Single Neuron." Fractal and Fractional, 2020.
- Bandyopadhyay, A. "A century-old picture of the nerve impulse is wrong: Filaments fire before the membrane, all filaments of all types fire together." Communicative & Integrative Biology, 2022.
Theoretical Foundations
- Berry, M.V. "Quantal Phase Factors Accompanying Adiabatic Changes." Proceedings of the Royal Society A, 1984.
- Gammaitoni, L. et al. "Stochastic Resonance." Reviews of Modern Physics, 1998.
- Naaman, R. & Waldeck, D.H. "Chiral-Induced Spin Selectivity Effect." Journal of Physical Chemistry Letters, 2012.
Feedback, corrections, and contributions are welcome. If you are an experimentalist with access to microtubule spectroscopy, we would be particularly interested in your assessment of the predicted resonance frequencies.