The brain is a fractal massively parallel processor generating complex spatiotemporal electromagnetic field patterns that correlate with cognition and perception. A key property of a fractal system is scale-free complexity, which means that the degree of complexity of the system is invariant under scaling— for example, using a power-law quantification, it can be shown that the degree of complexity within the human brain is approximately invariant from the tissue, to the cellular, to the molecular levels. The electrical field potentials and magnetic resonance responses of the brain all exhibit scale-free dynamics , and these scale-invariant brain dynamics contain complex spatiotemporal structures that are modulated by task performance. Previous studies have shown that scale-free temporal correlations connect the vibrational modes of single neurons to the fractal-antenna-like biopolymers (dielectric resonators), such as microtubules, within any single neuron, demonstrating a scale-free linking of dielectric resonances from the cellular to the molecular level in brain neurons .
Now, recent experiments performed by the Bandyopadhyay research group have directly measured a pair of electric field vortices generated by the actin intermediate filament grid-like network just below the neuronal membrane, which coherently activates all ion-channels in a circular area of the membrane lipid bilayer when an electrical signal propagates . Dielectric resonance images obtained by the research group showed that the ordered microtubule network in the core of the neuron cell body initiates and instructs a superstructure grid-like cylindrical network of beta-spectrin and actin intermediate filaments that interface with the neuronal lipid bilayer to generate a pair of electrical vortices, which in turn regulate the timing of the neuronal membrane’s electrical-ionic vortex signal. The findings are a continuation of the Bandyopadhyay research group’s empirical characterization and demonstration of microtubules and associated subcellular filamentary network’s direct role in the scale-free electromagnetic dynamics underlying cognition and perception within the brain , functioning as circular waveguides and resonators , as well as information processors .
Utilizing coaxial probe technology, with resolution at the nanoscopic scale, and dielectric resonance microscopy the Bandyopadhyay research group where able to investigate ultrafast communications of electromagnetic signals originating in the filamentary bundle of microtubules within single neurons to an actin grid-like network just below the neuronal membrane regulating the timing of action potentials. The researchers found that filamentary transmissions saturated 200 microseconds before the neuronal firing of an action potential, a time-domain that is 1000 times faster than the nerve spike. Nanoscale coaxial probe measurements at three simultaneous time-domains: milliseconds, microseconds, and nanoseconds resolved that the electromagnetic transmissions across tubulin proteins, microtubules, and neurons had a similar time-domain pattern in a scale-free triplet of triplet temporal pattern (Movie 1, Figure 2).
Movie 1. Frequency wheel for the triplet–triplet resonance frequency pattern for the four-4 nm-wide tubulin protein, for the 25-nm-wide microtubule nanowire and 1-μm-wide axon initial segment of a neuron. Reproduced from K. Saxena 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, vol. 4, no. 2, Art. no. 2, Jun. 2020, .
Figure 1. (a) 2D resonance of a single isolated microtubule, showing a triplet band of 10–300 kHz, 10–230 MHz and 1–20 GHz. A dotted line shows 1D resonance measurement location (top), the data are shown below panel (a). The 3D resonance plot of panel a is represented as a nest of nine circles (nine circles inside three circles inside one circle = 13 circles). A triplet in a 1D resonance plot of the panel is connected using a shadow and an arrow (a), with the schematic of panel (b); (c) The circular triplet–triplet plot of panel b is a replica of experimental resonance data (panel a), however, the resonant oscillations follow a periodic condition. If periodic limits are applied then panel b looks like panel c. One can find the triplet in panel c, each triplet has a single frequency, and its total period is the sum of three frequencies inside: each of the three has periods of eight frequencies (a particular case of tubulin). Reproduced from K. Saxena 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, vol. 4, no. 2, Art. no. 2, Jun. 2020, .
Movie 2. Triplet of triplet resonance bands in microtubule, animation showing the complex vibratory modes.
Utilizing the dielectric resonance imaging the researchers observed sections of the neurofilament-microtubule core, which acquired resonating electromagnetic energy, and due to the dielectric resonance and local symmetries of the helically oriented filaments selectively transported quantized energy through the subcellular network, contributing to the endogenous electrical field potential of the neuron. Then, by selectively resonating the beta-spectrin-actin cylindrical grid superstructure with the proper resonant frequency the researchers observed the formation of bright rings of electromagnetic vortices just beneath the plasma membrane (Figure 2). Importantly, the research team describes the precise topology of the propagating action potential as a ring of electric fields around the circular perimeter of the axonal branch, therefore propagating as a 3D Gaussian wave packet. This contrasts with the conventional neuronal model that solely considers neural transmissions as 1D spike potentials, which as the research group points out, does not comport with what happens in the network in a real-world scenario. As directly observed by the research team’s advanced methodology at nanoscale resolution, the nerve impulse is an electrical-ionic vortex that covers the perimeter of axonal or dendritic branches and is regulated by electromagnetic signals from the underlying subcellular filamentary network.
Figure 2. (A) Experimental setup for combined patch-clamp and coaxial probe measurement on a cultured plate. The recently invented coaxial atom probe senses several time domains at a time, even below 0.5 nm. Its cavity is between a Pt metal needle and an Au metal cylinder and traps (10−20 watt) vibrations in its vicinity, the cavity’s conical geometry amplifies that signal. The embedded dielectric resonator (glass) increases Q factor (~105) at all frequencies that its conical geometry allows (3 kHz to 40 GHz). Unlike the patch-clamp, an atom probe reads four signals simultaneously, filters the noise, measures four distinct vibrations of protein complexes, noise-free (S/N~105), deep inside a neuron. (B) Experimental setup for simultaneous microwave-radio wave combination with quantum optics. Monochromatic laser (633.5 nm) passes through vortex lens to generate optical vortex, that is shone on the axon region. A semiconductor camera images the reflected or transmitted vortex assembly. (C) A schematic of the neurofilament core, transporting resonant EM energy to the actin-beta spectrin intermediate filamentary superstructure, which coherently activates membrane ion channels to control for precise ionic firing time. (D) Two panels show that at the first step, beta-spectrin-actin Ring 1, Ring 2 are active, ions release in the circular pathway between them. Then Ring 1 switches off, Ring 2 and Ring 3 are active. Ion channels in between them are activated for ion release. Reproduced from P. Singh et al., “Cytoskeletal Filaments Deep Inside a Neuron Are not Silent: They Regulate the Precise Timing of Nerve Spikes Using a Pair of Vortices,” Symmetry, vol. 13, no. 5, Art. no. 5, May 2021, .
The Bandyopadhyay research group have described the importance of timing, or frequency, of neuro-filamentary electrical signals in generating the specific highly structured spatiotemporal electromagnetic field patterns of the brain. In fact, this has led the researchers to propose a self-operating time crystal model of the human brain, and they have discussed the possibility of completely replicating the cognitive functionality of the brain via a 3D fractal architecture of clocks alone . This highlights the significance of the team’s latest findings, as the electromagnetic vortices generated within the actin sub-membrane network produce a microsecond clock that regulates the millisecond ionic conduction of the neuronal axon. This finding is corroborative with previous research we have reported on such as multi-level subthreshold processing in dendrites, in which the complex subsynaptic architecture bestows on a single neuron the computational power normally attributed to entire multi-layered neuronal networks .
Bandyopadhyay’s research team describes the fractalized periodic oscillations from the microtubule to the actin and neuronal membranes as interconnected clocks, with the ordering and arrangement of the clocks revealing symmetry in the information structure of the neuron. The electromagnetic / optical vortex assembly is a geometric structure and by linking them with different symmetries of the neural architecture, a hardware perspective has been added to the observations of the collective signaling process in filamentary circuits. The researchers say that in the future they will perform research to better understand how the interplay and time-tuning mechanisms of the fractal clock architecture accounts for the entropy and thermodynamic responses of a neuron. And as their technology of the coaxial probe and dielectric resonance imaging advances, they hope to gain greater resolution of the subcomponents of the neuron to match each set of resonance frequencies to a specific subcomponent, further delineating the subthreshold dynamics regulating the electrical potential of the cell.
"The scale-free complexity associated with the biological system in general, and the neuron in particular, means that within each cell there is a veritable macromolecular brain, at least in terms of structural complexity, and perhaps to a certain degree functional complexity as well—an interconnected fractal architecture. This means that the extremely simplistic view of the synapse as a single digital bit is misrepresenting the reality of the situation—such as, if we were to utilize the parlance of the neurocomputational model, each ‘computational unit’ contains a veritable macromolecular brain within it. There is no computer or human technology yet equivalent to this."
– William Brown, Resonance Academy Big Questions Course, Lesson III: The Cellular Hologramic Information Nexus | Sentience and Memory Encoding in Cellular and Macromolecular Systems. 2018.
The complex spatiotemporal electromagnetic field patterns, which macroscopically form continuous waveforms, while microscopically are comprised of discrete electronic oscillations and electromagnetic vortices, are a direct indication of how the operation of the brain and cognition itself is field-like in nature. Behaviors of fields, like the electromagnetic field, contain an inherent kind of nonlocal quality, that is why they explain physical forces and seeming action at a distance. When considering the vacuum state of the electromagnetic field, it unambiguously is nonlocal, with intrinsic spatial correlation that connects systems regardless of spatial or temporal separation (see our article Quantum Energy Teleportation Protocol). This means that our minds are field-like, and operate much more like Rupert Sheldrake’s Morphic Resonance than the conventional neurocomputational model (Rupert Sheldrake has experimentally documented evidence of nonlocal signaling occurring in the brain and during animal cognition).
The field-like operation of the brain couldn’t be more evident than when considering the biophysics of the fractal antennae found at many levels of the neuronal system, from whole brain subregions to individual neurons, down to subcellular neuronal components. Many of these structures are dielectric resonators and have now been empirically documented as electromagnetic waveguides. These are the systems that couple biological functions to the field, which itself is comprised of harmonic resonators with hysteresis and memory functions—a reason why we refer to the fabric of space as spacememory.
Spacememory is the seat of intelligent processes in nature, and because of its vast interconnectivity and nonlocality in space and time, it is a domain of natural hyperintelligence. It is no surprise then that the information processing structures of the biological system are specifically coupled with the field, as the biological system emerged from and evolved with the hyperintelligent network of the field. Even the electromagnetic vortices described by Bandyopadhyay’s research team is a testament to this, as the torus dynamic is a key integral feature of the fundamental geometry of spacetime, such that an electromagnetic vortex within the neuron is inducing a toroidal dynamic of the Planck Plasma, for maximal coherent energy transmission and collective synchronization.
 B. J. He, “Scale-Free Properties of the Functional Magnetic Resonance Imaging Signal during Rest and Task,” J. Neurosci., vol. 31, no. 39, pp. 13786–13795, Sep. 2011, doi: 10.1523/JNEUROSCI.2111-11.2011.
 K. Saxena 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, vol. 4, no. 2, Art. no. 2, Jun. 2020, doi: 10.3390/fractalfract4020011.
 P. Singh et al., “Cytoskeletal Filaments Deep Inside a Neuron Are not Silent: They Regulate the Precise Timing of Nerve Spikes Using a Pair of Vortices,” Symmetry, vol. 13, no. 5, Art. no. 5, May 2021, doi: 10.3390/sym13050821.
 S. Sahu, S. Ghosh, K. Hirata, D. Fujita, and A. Bandyopadhyay, “Multi-level memory-switching properties of a single brain microtubule,” Applied Physics Letters, vol. 102, no. 12, p. 123701, Mar. 2013, doi: 10.1063/1.4793995.
 F. Jelínek and J. Pokorný, “Microtubules in Biological Cells as Circular Waveguides and Resonators,” Electro- and Magnetobiology, vol. 20, no. 1, pp. 75–80, Jan. 2001, doi: 10.1081/JBC-100103161.
 T. J. A. Craddock, C. Beauchemin, and J. A. Tuszynski, “Information processing mechanisms in microtubules at physiological temperature: Model predictions for experimental tests,” Biosystems, vol. 97, no. 1, pp. 28–34, Jul. 2009, doi: 10.1016/j.biosystems.2009.04.001.
 P. Singh et al., “A Self-Operating Time Crystal Model of the Human Brain: Can We Replace Entire Brain Hardware with a 3D Fractal Architecture of Clocks Alone?,” Information, vol. 11, no. 5, Art. no. 5, May 2020, doi: 10.3390/info11050238.
 A. Gidon et al., “Dendritic action potentials and computation in human layer 2/3 cortical neurons,” Science, vol. 367, no. 6473, pp. 83–87, Jan. 2020, doi: 10.1126/science.aax6239.