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Fig. 1. The trace of the image of a particle in the cross section of torus: x> 0.

             Definitions and Notations:

x = 2 (μ2/μ1) –Dissymmetry coefficient, where μ^ = μ1 + i• μ2 is the coefficient of the point quadratic Poincare map in the iteration equation (1) determined

by the parameters of μ ^ homeostasis, see [4]:


            z(n+1)= μ•z(n)•(1- z(n))             (1)

Here n is the ordinal number of the iteration, which has the meaning of discrete biological time; μ = μ1(ξ, Θ) + i•μ2 (ξ, Θ) is a complex function of  2 parameters (ξ, Θ), where ξ is a generalized indicator of human homeostasis [3,4], Θ is an empirical function of acid and alkaline equilibrium of 2 body fluids, blood -pH and liquor -pD.


It is shown that in the momentum space of states, a human BP image has the form of a fractal. The fractal BP image of H. sapiens can be used not only in psychiatry. It can be used also in oncology, in the cancer diagnostics and in bioresonance therapy– upon treatment of any diseases. As an illustration of the above mentioned, Fig. 1 shows a fractal image of a patient who had had (at the time of diagnosis)

the following characteristics:

k=1, N=4.17, f=84 [beat/min], alf=8.25, pH=7.4.


Here alf is the reduced resonant frequency of the ‘alpha’ rhythm, which is associated with a person the mental activity - see above. And such a connection is biologically justified. One of the sages had said: “I think therefore I am alive!”

 * NOTE: As we know the BP amplitude at the "alpha rhythm" frequencies of sleeping

and blind people is close to zero.



Let the mathematical expectation of the pain force F coincide with the result of the patient survey R, made on a visual analogue scale. Then the shape of the bioelectric potential, the pain index R and the fractal image of the human being, Fig. 1 (2,3), will be determined by a complex value µ^, which takes the next form [3,4]:

μ1=α•ln(R);     μ2= 1+ S(δ) - 0.09•(√R/(√ξ),       (2)

where, as it was before, α=0.85, ξ is the generalized index of homeostasis, being a solution of the Hamilton equations (arch. file Terepa-111).




k is the blood group number, N is the concentration of blood plasma red cells, f(p) is the pulse rate; f(a) - rhythm frequency "alpha"; alf is the reduced rhythm frequency "alpha"; ph, pD - indicators of acid-base balance of blood and HPA; S(δ) standard mathematical function "integral sine" [8]; δ is defined as the offset of the difference

frequency of the radiation from zero:

                         δ = √q  - √qo, 

q=2•f(a)/f(p),   f(p) = f[Hz],   f(a)=alf*(π/2);

qo =21.8 – square of Feigenbaum constant.



x= 0.66, Q=0.75.




Yoga teachers tell their students “to in the stream." But, for some reason, they do not specify what kind of flow is being meant?


Apparently, we are talking about the flow of Prana, the informational part of the torsion field energy, which permeates the physical body from top to bottom

or from bottom to top.


The energy flow of any vector field is calculated using the so-called Umov-Poynting vector [9]. The density of the flow of kinetic energy of the electric charge rotation corresponds to the number of black (in the inverse image - white) pixels per square

cross section of torus Fig.1 (2, 3).

To obtain a more complete picture of the biopotential, it is useful to consider the physics of the interaction of the latter with the Earth's torsion field in the space of frequencies, having 3 dimentions.

Let T(k) be the energy of the T-field at one of its eigenfrequencies, and let W (k) be the wave energy of the H. sapiens at a frequency, depending on the wave number k*.

Let’s imagine a partial biotorsion field W(J) through the interaction matrix M:




Here k=1 is the rhythm of the Earth's crust “breathing” (lungs + bronchi), k=2 is el. osc. of T-fields at the heart rate (heart + vessels). Heart rate driver, k=3- the T-field vibrations at the"alpha" rhythm; k=4 – higher order frequency rhythm.

In the first approximation, matrix M off-diagonal coefficients will be considered as equal to zero. As a result the total energy of an individual’s biotorsion field (BP energy) turns out to be a linear superposition of the energy of, at least, 3 components of the Earth’s crust torsion field (4). Therefore the whole wave

energy of an individual consists of:

1) respiratory energy W[1]=α(1,1)●T[1],

2) biotorsion energy of heart beating W[2]=α(2,2)*T[2],

3) high-frequency component of the kinetic energy of a particle rotation with a rhythm frequency alpha W[3]:

Wo= α(1,1)•T[1] + α(2,2)•T[2] + α(3,3)•T[3].                (4)



 * NOTE: The left-hand side of equation (4) is the frequency function Wo, which has local maxima at 3 frequencies. If the diagnosis of human health is carried out at low frequencies,  then under resonance conditions the “indicator” of the control energy of consciousness is the auto-oscillation of the biopotential at the rhythm frequency “alpha”

Let us add that some part of the wave potential is inherent not only to the SAU, i.e. to the pineal gland, but also - to other organs: the heart, lungs, bronchi, liver, etc.


 Additions. Illustrations.


It should be noted that the version of the Health care  index program, presented here, does not requires generating of a patient fractal. Therefore, the statistics of clinical observations of patients allows to calculate the Health Index making use of  the empirical function Q(x) to simplify statistical results of the method, see Fig. 3.


Fig. 3. Dependence of the Health Index on the dissymmetry coefficient.


The vertical x = 0 in Fig.3 divides the plane {Q,x} into the two regions with different signs of polarization instability decrement. To the left of the vertical the increment of the increase of energy, entering the living organism from the T-field, is replaced by the decrement of energy attenuation stored in the biophysical system of field energy, which is consistent with the phenomenon of the existence of negative entropy, the so-called non-heterotrophy of living systems.




The case of mirror asymmetry (left <=> right).


There are TWO different approaches to determining the energy of an imaging particle rotating along a Human being Spinal chord.

According to the first approach, a health index is the value of the dissymmetry coefficient function Q (x), where x = 2•(μ2/μ1). The 2nd evaluation method consists in calculating of the fractal dimension of the last set of pixels. The 2nd  method of Health indexing is equivalent to the first one.

Let's try, at least roughly, evaluate the energy of the psychic component of BP. According to the previous, so called PSI energy of thought is represented by two 3rd-order vortices. In total, the area of all third-order vortices, evaluated in relative units, is approximately 0,1 of the total energy of the particle.

The article was provided by Prof. M.V. Kutushov on 15.09.2017.


[1]. “Numeric code for constructing fractal images of H. sapiens”, access to the computing algorithm;

[2]. P.I. Kurilko “Generation of a fractal by the frequency of α-rhythm radiation”;

[3]. P. Kurilko, M. Kutushov “FRACTAL PHYSICS”,, June 2017;

[4]. M. Kutushov, P. Kurilko “Fractal Geometry in Health Diagnostics”, “Exact Science”, Kemerovo, ISSN 2500-1152, Issue No. 10, 2017;

[5]. N.V. Butenin, N.A. Fufaev “Introduction to Analytical Mechanics”, Chapter 4: “Canonical Equations of Perturbed Motion”, p. 174, “Nauka”, 1991;

[6]. P. Kurilko et al., “About Role of the Pain Psychogenic

Component in the Cancer Development”;

[7]. A.Yu. Loskutov, A.S. Mikhailov, “Introduction to Synergetics”, UDC 530.1 (075.8), 272 pages, Moscow, Nauka, 1990;

[8]. G. CORN, T. CORN “Handbook of Mathematics”, 1968, chapter 15, p. 485;

[9]. Umov–Poynting vector, Wikipedia, August 2017;

[10]. Smale-Williams’ solenoid, Wikipedia

Bifurcation of double frequency

BIOTORSION FIELD of Homo sapiens at the MODEL by Dr. KUTUSHOV.


  • The Conducted Measurement of the Biotorsion Field of an Individual.

  • Dependence of the Health Index on the Dissymmetry Coefficient.

  • Fractals.

The measurement of the biotorsion field of Homo sapiens (H. sapiens) which is considered as the indicator of his general medical condition including checking the patient oncologic status has been held within the framework

of the fractal biophysical model of a human being.


Anatomy is the basis of modern medical science. However, without the basics of physiology, anatomy becomes a "transcendental object." And it requires the involvement of physiology. The latter pulls biology with biophysics and biochemistry. At the intersection of medicine and rhythmology, a separate direction has appeared - biorhythmology. The study of H. sapiens biorhythms involves the consideration of a human being as an auto oscillating system (abbr. AOS). The simplest physical model of the AOS is a bioresonant circuit with an oscillating platform, which is represented by a fragment of the earth's crust. Without conducting special studies, it can be assumed that the spectrum of natural electric oscillations of the pendulum will depend on the Earth platform spectrum of its natural oscillations*.

* NOTE: Auto oscillations of a system are called as its own, if they depend only on the properties of the system itself and do not depend on the frequency

of an external driving force.

At the 1st approximation, the authors have shown the frequency spectrum of H. sapiens biopotentials coincides with the spectrum of the Earth's crust oscillations. (For example, if a person’s heart is contracting with a frequency of 1 Hz, then there can be no doubt that the same frequency also presents itself in the Earth's crust). So, between the Earth and a human being takes place an electromagnetic field interaction. On the other hand, a similar (above mentioned) interaction has place between individual’s human being organs. Until now we have proved well-known facts to be included in the textbooks on the biology and physics of the Earth crust.

The mechanism of resonant interaction between two organs of the same individual is much less known. Let x be a typical size of organ N 1; ω, λ are the frequency and period of the radiation of the organ N 2, to  influence at the organ N 1. Let p be an impulse of a solitary wave. The phase speed of potential’s wave is V = p/m, where m = 1 is the inertial mass, equal to 1. Under conditions when the parameters of the biophysical system (speed and wavelength, density of a liquid crystal plasma, the typical size of a biophysical object - organ N 1) satisfy to the Cherenkov ratio

        (1)ˆ             ω=2π•(v/λ),  

an effective transfer of energy from an external field to organ N 1 and vice versa is expected. For the "putting" into the work of the resonance interaction mechanism, it is required to provide a  geometric ratio: λ = x. Taking into account the definition of impulse, v =p/m with m = 1, the Cherenkov resonance condition (wave + organ) takes the following form:

        (2)ˆ                   ω=2π•(p/x).

Let’s rewrite (2) in the form: p = x • (ω)/ 2π. Hence it follows that the amplitude dependence of the charge particle kinetic biopotential on frequency (AFC) is equivalent to the wave particle kinetic energy distribution on its impulses.


The interaction between different organs and systems of a person in dynamics requires a frequency adjustment of the so-called ‘pumping field’. It is important to note here that such an external pumping field restructuring does not occur smoothly, adiabatically, but abruptly. Experience has shown that the excitation frequency either doubles or reduces twice. The indicated phenomenon is known in the annals of physical science as bifurcation (doubling) of an oscillation period (O. Ressler). Physicists have established a law that states: the 4-th frequency bifurcation leads to chaos. It leads to the auto oscillation cycle destruction. However, after the Ressler’s discovery the phenomenon of generation of a chain of frequency period doubling/ splitting, had been discovered which was called Feigenbaum's “cascade of bifurcations” [2]. The indicated discrepancy between the scenarios [1] and [(2)] prompted the authors to conduct their own investigation of the discrepancy.


In the course of author’s research, the so-called teen-furcation frequency phenomenon had been discovered (unpublished), to be discussed in the Section 3.

A cascade of bifurcations of frequency doubling arises automatically, on its own. The biological expediency of doubling is to distribute the energy of a solitary wave of "pumping" evenly throughout the body in accordance with the fractal structure of the latter. The novelty of our result is as follows. The fractal configuration of human organs and tissues is reliably known.

But, the fractal configuration of the H. sapiens biological potential and the wave interaction of organs and subsystems remain, by now, practically unknown in practical medicine*.

Due to relevance of the last information about H. sapiens fractality we focused our efforts on studying of the biopotential (abbr. BP) fractal structure. The main goal of studying of BP structure consists in the necessity to assess the correlation measure of wave interaction between different organs and systems of a person.

*The aim of this work is to develop a method of fractalography that is to find a way to health notation using a mathematical model of biotorsion (information) field.

3. “T-FURCATION” by Kurilko-Kutushov.

The novelty of this work is that we discovered the phenomenon of the 2nd second order bifurcation. The essence of the discovery is following. In the chain of period doubling the own frequency of a Ressler resonance circuit,

every 4th doubling appears to be resonant! In order not to confuse the latter with the usual Ressler-Feigenbaum bifurcation, we shall call it “teen-furcation” from the English “sixteen”: 2*2*2*2 = 16.  By virtue of the fractal

configuration of the H. sapiens physical body each anatomical structure will have its own resonant frequency of teen-furcation by Kutushov.


   Let x = a be the radius of the cross section of the physical body. Then, in accordance with (1), each frequency of teen-furcation from the whole spectrum will correspond to an eigenvalue of the solitary wave momentum. Let's put in a solitary wave of BP the so-called image particle, with fixed phase of the wave phase. Then, mathematically, our task is reduced to finding the trajectory of the charged particle in the momentum space. It should be noted that the momentum space is 3-dimensional one. But for the beginning, for simplicity, it will be quite enough to build a two-dimensional trace projection of the desired trajectory onto the drawing plane,

similar to the FIGURE 1 (2, 3).

Let’s take into account that the type of trajectory will depend on the characteristics of the environment - the basis of which is a hydroprotein complex, HPC, which means

a suspension of proteins and structured water

Math. characteristic of HPC is an integral pointer of dissymmetry x(t). Our methods of fractal health diagnostics are based on this measured dependence

of the generating function x (t).

The method for a fractal reconstructing is described in more detail in the Section 4. It should be born in mind that the form of the fractal depends on the dissymmetry coefficient (3). The method for calculating of this coefficient

is discussed in the Appendix 1.


In quantum physics the behavior of a system, consisting of interacting particles, can be represented by the Hamilton equations of motion in the "coordinate - momentum" variables. For one depicting particle, and this is just our case, the total number of unknown values is equal to 6:

           x[1], x[2], x[3], p[1], p[2], p[3].  

On top of all, it remains to state that by combining the projection of the particle trajectory with the plane of the drawing, we obtain a fractal image of the biotorsion electromagnetic field in the "PD" dimension! Compare our result with its prototype. As a prototype, one can consider the amplitude-frequency characteristic of the alpha rhythm, AFC, the frequency response received by a Russian biophysicist E. Maltseva 15 years ago [8]. Using a high-resolution frequency meter the scientist showed that the AFC of this biorhythm is a linear fractal. At the same time, it was proved by numerical experiments (the “TEREPA” file) that the alpha-type rhythm exists in the model of elastic oscillations of the electric potentials of the T-field of the Earth's crust. Thus, the result of this research is a generalization of [8]

the results for the space of 2 and 3 dimensions.


The complete system of particle motion equations consists of 11 non-linear Hamilton differential equations [9]. The 1st task had come to definition of the so-called summarized index of homeostasis ξ which is required for the fractal generating conducted using the iteration equation [1].


Under an imaging particle we will consider a test charged particle, the velocity and momentum of which are determined by the iteration equation

as function of discreet time.


An example of a depicting particle is a luminous spot on a radar screen, which is a radio signal wave reflected from an airplane.

The projection of the imaging particle trajectory onto the plane of the constant phase Ψ is shown in the Fig.1. In the first approximation the effect of the torsion field rotation over the Earth's crust with time t can be modeled by uniform rotation of the reference frame (coordinate system) around the main axis of the torus with a speed of Vo. In a rotating inertial coordinate system, centered about a point, a charged particle, under the action of a T-field, will either accelerate or slow down along the torus, having its variable speed V(t), and also will have rotation on azimuth and participate in oscillations on a small radius of the torus:  


It is the variations in the velocity of longitudinal motion that induce the imaging particle to cross the plane of the constant phase, leaving in it traces in the form of discrete points –pixels, that create a pattern called FRACTAL*. Let us recall that a charge particle of liquid crystal plasma (a solitary wave of charge density) moves in the physical body of H. sapiens under the action of the torsion field of the Earth's crust.  When repeatedly   passing   around   the   torus {X(t), Y(t), t}, t → ∞, the particle "embroiders" a pattern that has the signs of a fractal.


Formally, a fractal by Kutushov-Kurilko, abbr. KK, is a discrete set of fractional dimension. The method for constructing of PK fractal needs to be explained. The connected set of all points of the ellipse by Kutushov

in the Fig. 1, has the topological S=2 dimension of TWO.

However, in the most general case, not all ellipse points will belong to a discrete set. (And, accordingly, not all of them will be highlighted in black color!). The criterion for the belonging of points of the set of to the fractal PK is the deviation of its real dimension from the topological one, which is an integer value: s=2. The question is HOW to determine the fractional dimension of the fractal?

In order to obtain a fractional dimension from formal point of view, it is necessary to calculate the ratio of the number of "fractal" pixels to the total number

of pixels "covering" the area of the ellipse shown in Fig. 1.

In fact this ratio is not an integer, but a fractional number. Calculation of fractal pixels number requires an indication of the criterion of each selected point of the so-called pool (ellipse by Kutushov) belonging to a certain condition

applied to the particle velocity v(t).

In the task of fractal rebuilding the limited rotation of the imaging wave particle energy over the small azimuth of the Smale-Williams solenoid [*]

is a precondition of a point belonging to the fractal.


Mention of the torsion field (PRANA) is found in esoteric and the Yoga teaching literature [9]. The physics of this primary energy - PRANA, produced by the Earth's torsion field [5], is clear. But we will not go deep into the origin of Prana. Let's move on to the equation for fractals generating and solving of this equation.

Fig.1 shows the trajectory of a particle moving in the so-called “PM” dimension {X = m●V (x), Y = m●V (y), t], which represents the auto oscillations of its momentum. The particle kinetic energy is composed of the energy of 4 solitons - vortices

of the 1-st, 2-nd, 3rd, 4-th (and higher) orders.

 * NOTE: Each vortice has its own combination frequency: k = 1,2,3,4, ….

"T-Furcation" by Kurilko-Kutushov
Formulation the tas
Results discussion
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