CN104091057A - Method for generating fractal unit matrix and growth matrix of special energy gathering structure - Google Patents

Abstract

The invention discloses a method for generating a fractal unit matrix and a growth matrix of a special energy gathering structure. The method includes the following steps that first, digital quality of each element of the fractal unit matrix is defined; second, a growth matrix is determined, wherein the growth matrix with any i-dimension special energy gathering structure parameters is derived; third, whether the designed parameter matrix meets the requirement for optimization of a parameter matrix of the special energy gathering structure or not is checked; fourth, the parameter matrix of the special energy gathering structure is determined, wherein after a physical quantity is selected, the constant c is determined, and the parameter matrix of the designed structure is obtained; fifth, the material for use, the total size and the shape of the special energy gathering structure and the shape and the size of each structural unit are designed as required. The method for generating the fractal unit matrix and the growth matrix of the special energy gathering structure has the advantages that generation of the energy gathering structure is irrelevant to the material, the shape and the size of the made structure but only relevant to the sequence of all constitutional units of the structure.

Description

The production method of the fractal cell matrix of special cumulative structure and growth matrix

Technical field

The present invention relates to signal processing technology, the application of the application of fractal theory and complex system modeling theory, particularly a kind of production method with the fractal cell matrix of fractal characteristic and the matrix of growing.

Background technology

Different structures can cause different physical characteristicss, and complicated nonlinear system is because the difference that puts in order of its component units can cause the different impact on signal, and some special structures also have very strong energy effect.At present for structure, system, the research of the relation of information and energy at home and abroad also seldom, such as No. 94117538.3 patent < < universe energy collector > > of Chinese invention patent, a kind of structure being formed by 64 metal cylinders of the Patent designs such as No. 200410102761.4 < < energy gathering type field effect instrument > > and United States Patent (USP) No. 7445009 " Spatial field effect physical therapy device ", in the clinical practice of experiment and reality, show that this structure periphery has the effect of energy accumulating, can amplify electromagnetic signal.But these patents are not analyzed this special feature that has cumulative effect structure, feature, and the Physical Mechanism of its work is not described yet.

According to principle of maximum entropy, when the feature of system is evenly distributed, system reaches equilibrium state, and entropy is now maximum.The designed special cumulative structure of the present invention has symmetry and the balance of height, each eigenwert equiprobability appearance of structural system, and this structure has maximum characteristic information entropy.Therefore information entropy maximum is exactly the objective function in design of Structural Parameters of the present invention, constraint condition is that feature set has each and equates to digital density, the mathematical iterations formula of the growth matrix of this structure belongs to pioneering, and the growth matrix producing according to this mathematical iterations formula and the parameter matrix of structure design the structure called after " special cumulative structure " of realization.

The research of fractal theory and application thereof has obtained significant achievement in many aspects, in to the analysis of complex network, find that in real world, a lot of networks are fractal net work, there is certain inherent self-similarity, disclose in complex network without the relation existing between characteristics of scale and fractal property, the research that fractal theory is complex network provides new angle.Utilize the fractal characteristic of system to be more convenient for network to carry out modeling and analysis, first the present invention has carried out characteristic analysis to this special cumulative structure, points out that this structure has fractal characteristic, local and local, between part and integral body, exists self-similarity.Then utilize this self-similarity, set up the mathematical model of special cumulative structure, derive the mathematical iterations formula of the parameter matrix of special cumulative structure.

This have a fractal characteristic, there is special cumulative structure highly symmetrical and balance simultaneously and can assemble electromagnetic energy, and electromagnetic signal is had to amplification, this structure requires limitation very little to material and shape, can be that spatial structure can be also planar structure, as long as put in order mathematical iterations formula according to the invention and the constraint condition of the ingredient of structure, just have the function of assembling electromagnetic energy and amplifying electromagnetic signal.Can need to amplify and the field of focused energy electromagnetic signal for various, have very strong practicality and wide application prospect.

Summary of the invention

The object of the invention is to utilize fractal theory and principle of maximum entropy, a kind of fractal cell matrix of special cumulative structure and the production method of growth matrix are provided, in the method, the parameter of structure has fractal characteristic, the invention provides the mathematic(al) representation that produces the fractal unit of this special cumulative structure, and the growth matrix of this special cumulative structure and mathematical model and the alternative manner of this structural parameters matrix of design are provided.This structure can be assembled the various electromagnetic energies in space, and there is time delay memory function this structural energy field and various electromagnetic signals are had to amplification, and the electromagnetic screen net that this special cumulative structure can penetrating metal around acts on it.The parameter matrix being produced by mathematical iterations formula of the present invention, meet the constraint condition of this structure in the present invention and design the structure of realization, there is special energy accumulating effect, the invention belongs to pioneering, this structure is because being different from other the structure that can assemble electromagnetic energy, so called after " special cumulative structure ".The present invention provides the condition that meets special cumulative structural parameters, and the condition that obtains optimum cumulative effect.This special cumulative structure can be applicable to each relevant field that needs focused energy and electromagnetic signal is amplified, and to analysis of complex system.

Object of the present invention is achieved through the following technical solutions: the production method of a kind of fractal cell matrix of special cumulative structure and growth matrix, by structural parameters matrix computations provided by the invention, go out and generate required parameter, according to application and occasion selection material, press the required special cumulative structure of parameter matrix Design and implementation generating, specifically comprise the steps:

Step 1, determine fractal cell S _i, definition matrix X=(x _ij) the digital quality of each element be m:

m＝x _ij， (1)

The path of definition from an element to another element is l _n, l _nlength by the number of elements n of process; The digital density that defines this line segment is:

${\mathrm{\&rho;}}_l=\frac{{\mathrm{\&Sigma;m}}_{\mathrm{ij}}}{n},---\left(2\right)$

The parameter matrix of special cumulative structure has fractal characteristic, and its fractal unit is that the mutually orthogonal and equal in length straight-line segment of two digital equal densities forms.The parameter matrix of special cumulative structure has fractal characteristic, and the affine variation of its two dimensional surface is:

$W\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}e\\ f\end{array}\right)=W\left(X\right)=A\left(X\right)+T,---\left(3\right)$

Wherein, $A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right),X=\left(\begin{array}{c}x\\ y\end{array}\right),T=\left(\begin{array}{c}e\\ f\end{array}\right);$

A, T are desirable:

Convergent-divergent $A_1=\left(\begin{array}{cc}k& 0\\ 0& k\end{array}\right)$ (k is integer), rotation $A_2=\left(\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right),\mathrm{\&theta;}=\frac{\mathrm{\&pi;}}{2}l.l\&Element;N,$ Translation $T=\left(\begin{array}{c}m\\ n\end{array}\right),m,n\&Element;N;$

In sum, the parameter matrix of special cumulative structure is a kind of matrix having as shown in Fig. 2 (a), Fig. 2 (b) and Fig. 2 (c).

Special cumulative structure has symmetry and the balance of height, and according to principle of maximum entropy, the system features of this structure is evenly distributed, and has maximum characteristic information entropy.The feature set of therefore, establishing its parameter matrix is: S _i=(s _i1s _i2s _i3s _i4s _i5s _i6s _i7s _i8) _{1 * 8}, s wherein _ij∈ N (integer).Element s _ijrepresent the feature classification of special cumulative configuration state, the characteristic information entropy of this structure is:

$H\left(T\right)=-\underset{j=1}{\overset{8}{\mathrm{\&Sigma;}}}p\left(s_{\mathrm{ij}}\right)\mathrm{lbp}\left(s_{\mathrm{ij}}\right),---\left(4\right)$

Wherein:

$p\left(s_{\mathrm{ij}}\right)=\frac{w_{\mathrm{ij}}n\left(s_{\mathrm{ij}}\right)}{\underset{j}{\mathrm{\&Sigma;}}{w}_{\mathrm{ij}}n\left(s_{\mathrm{ij}}\right)},---\left(5\right)$

Probability p (s _ij) be status flag s _ijat feature set S _ithe proportion of middle appearance, w _ijit is weighting coefficient.

S _ielement can form matrix $F=\left(\begin{array}{ccc}{s}_{i1}& s_{i2}& s_{i3}\\ s_{i8}& 0& s_{i4}\\ s_{i7}& s_{i6}& s_{i5}\end{array}\right),$ F will reach maximum information entropy, and F should have each to the symmetry of digital density, and each w _ijvalue equate, make each s _ijp (s _ij) equate.S _ishould meet (6) formula determines:

s _i1+s _i5＝s _i3+s _i7＝s _i4+s _i8＝s _i2+s _i6， (6)

So S _ieach element be a solution of (7) formula;

$\begin{array}{c}\max H\left(S_i\right)\\ s.t.\left\{\begin{array}{c}{s}_{i1}+s_{i5}=s_{i3}+s_{i7}=s_{i4}+s_{i8}=s_{i2}+s_{i6},\\ s_{\mathrm{ij}}\&GreaterEqual;0,s_{\mathrm{ij}}\&Element;N\end{array}\right.\end{array}---\left(7\right)$

(7) the Xie Shi gang of formula separates, and can therefrom choose a suitable solution, execution step two;

Step 2, determine growth matrix, find the iterative manner of special cumulative structure, derive and obtain the growth matrix Y that i arbitrarily ties up special cumulative structural parameters ⁱ, the S calculating according to step 1 _ican obtain the growth matrix that i ties up special cumulative structure is formula (8):

$\begin{array}{c}{Y}^1={\left(\begin{array}{cccccccc}{y}_{11}& y_{12}& y_{13}& y_{14}& y_{15}& y_{16}& y_{17}& y_{18}\end{array}\right)}_{1\&times;8},(i=1),\\ Y^i={\left(\begin{array}{c}{s}_{i1}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i2}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i3}{E}_{(i-1)\&times;8}{+Y}^{i-1}\\ s_{i4}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i5}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i6}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i7}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i8}{E}_{(i-1)\&times;8}+Y^{i-1}\end{array}\right)}_{8^{i-1}\&times;8}\end{array}(i\&GreaterEqual;2),---\left(8\right)$

Y ⁱfor the i long matrix of supporting one's family, wherein: E _{i * j}that to tie up whole elements be 1 matrix to i * j; Y ¹requirement and the S of described step 1 _iidentical, Y ¹=(y ₁₁y ₁₂y ₁₃y ₁₄y ₁₅y ₁₆y ₁₇y ₁₈) _{1 * 8}for one-dimensional growth matrix, be called for short Y, wherein, s _ij, y _ij∈ N.If that required is the special cumulative structure of one dimension, Y ¹=S _i, directly use the determined S of step 1 _i=(s _i1s _i2s _i3s _i4s _i5s _i6s _i7s _i8) _{1 * 8}; If designed is the above special cumulative structure of two dimension, by (8) formula, determine growth matrix;

Step 3: whether the parameter matrix of inspection institute's design meets the optimized requirement of special cumulative structural parameters matrix;

The parameter growth matrix of special cumulative structure has following three features, and these three features can be used as the growth matrix of inspection institute's design and the condition whether parameter matrix meets special cumulative structure;

Condition (1): growth matrix has the described fractal characteristic of described step 1;

Condition (2): because the feature set of parameter matrix is obtained by formula (7), the solution of formula (7) is not unique solution, so want the structural parameters matrix that inspection institute obtains whether to reach optimal value.

Definition matrix Y ⁱthe digital quality of each element be m _ij, Y ⁱtotal digital quality be G (Y ⁱ):

m _ij＝y _ij， (9)

$G\left(Y^i\right)=\underset{i,j}{\mathrm{\&Sigma;}}{m}_{\mathrm{ij}}=\underset{i,j}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}},---\left(10\right)$

Growth matrix Y ⁱthe digital barycenter of all elements at how much barycenter places of structure;

Condition (3): be to obtaining matrix after each element delivery 5 of growth matrix the digital barycenter of all elements is still at how much barycenter places of its structure;

If designed special cumulative structure reaches optimal value, S _i, Y ¹meet (7) formula and (8) formula, will meet three above-mentioned conditions simultaneously;

Step 4, determine parameter matrix, according to application, determine the parameter matrix of special cumulative structure, each element in parameter matrix is the parameter value of each unit of special cumulative structure, determine as required this parameter be area, volume, highly, strength of current, wave frequency or other required various physical quantitys, select after physical quantity, determine constant c (c is plural number), obtain the parameter matrix formula (11) of designed structure:

X＝cY ⁱ， (11)

Shape and the size of step 5, the material therefor that designs as required special cumulative structure, overall dimensions, shape and each structural unit.

The present invention has following advantage and effect with respect to prior art:

(1) this structure periphery has energy accumulating phenomenon, and composition comprises the electromagnetic signal of various frequency ranges and other principal component not that may exist after tested.

(2) this structure can be amplified the electromagnetic signal of multiple frequency range.

(3) this structure is after removing, and original place energy field has memory delay function, still has a period of time.

(4) the penetrable metal of the energy field of this special cumulative structure, still has features above-mentioned (1), (2), (3) by metallic shield in the situation that in this structure.

(5) above-mentioned 4 have nothing to do with material, shape, the size of making structure itself.The sample that this structure is used the multiple materials such as various metals, mineral crystal, wooden, macromolecular material, cement to make carried out test, and above 4 features all exist.

Accompanying drawing explanation

Fig. 1 is the special cumulative of a kind of two dimension structural plan design drawing.

Fig. 2 (a) is l _n=8 special cumulative structure fractal characteristic schematic diagram.

Fig. 2 (b) is l _n=4 special cumulative structure fractal characteristic schematic diagram

Fig. 2 (c) is l _n=2 special cumulative structure fractal characteristic schematic diagram.

Fig. 3 is the special cumulative structural parameters of a kind of two dimension list figure.

Fig. 4 is the Electric and magnetic fields increment of the special cumulative superstructure shown in Fig. 1, unit: DB.

Fig. 5 is the power increment of the special cumulative superstructure shown in Fig. 1, unit: microwatt/square metre.

Fig. 6 is the memory delay time of the special cumulative structure shown in Fig. 1, unit: second.

Fig. 7 is the electric field intensity increment that the special cumulative structure shown in Fig. 1 is placed on the gauze screen outside of testing in metallic shield net, unit: DB.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

As shown in Figure 1, the special cumulative structural design of a kind of two dimension of the present invention is set S with single-side coated copper plate by described step 1 _i=(3 827164 9)=Y ¹, S _imeet formula (7).

By formula (8), calculate two-dimensional growth matrix: $Y^2={\left(\begin{array}{c}3E_{1\&times;8}+Y^1\\ 8E_{1\&times;8}+Y^1\\ 2E_{1\&times;8}+Y^1\\ 7E_{1\&times;8}+Y^1\\ E_{1\&times;8}+Y^1\\ {6E}_{1\&times;8}+Y^1\\ {4E}_{1\&times;8}+Y^1\\ {9E}_{1\&times;8}+Y^1\end{array}\right)}_{8\&times;8},$

By formula (11), calculate the parameter matrix X=4Y of this structure ², each element of X as shown in Figure 3.

By each element value that calculates parameter matrix X, produce 64 rectangles that vary in size, with each rectangle interval of a line, be 2mm, structure overall dimensions is 80 * 80mm rectangle, and structure as shown in Figure 1.Structure consists of 64 little rectangles, and the black part in Fig. 1 is divided into covers copper part, covers the area data of copper rectangle as shown in form in Fig. 3, and unit is mm ².

This Y ²the condition (1), (2) and (3) that meet described step 3.

Carry out contrast test with smooth copper-clad plate, test signal is 50MHz-3.5GHz, and test result as shown in Figure 4, Figure 5, Figure 6 and Figure 7.Fig. 4 is structure shown in Fig. 1 and the electric field intensity of smooth copper-clad plate contrast and the increment of magnetic field intensity, and test result illustrates that this structure has obvious enhancing effect to electromagnetic signal.Fig. 5 is the increment of the power density of structure shown in Fig. 1 and smooth copper-clad plate contrast.Fig. 6 is after withdrawing the special cumulative structure shown in Fig. 1, still has energy field to exist in sample original place, signal is still had to enlarge-effect, energy field delay time τ ≈ 380 seconds.The result of Fig. 7 be after the sample penetration metallic shield of special cumulative structure with the electric field intensity contrast of smooth copper-clad plate, result shows the signal effect of the penetrable metallic shield of the energy of this structure sample to structure periphery.

Above-described embodiment is preferably embodiment of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (6)

1. a production method for the fractal cell matrix of special cumulative structure and growth matrix, is characterized in that, comprises the steps:

Step 1, determine fractal cell S _i, define fractal cell matrix X=(x _ij) the digital quality m of each element:

m＝x _ij， (1)

The path of definition from an element to another element is l _n, l _nlength by the number of elements n of process; The digital density that defines this line segment is:

${\mathrm{\&rho;}}_l=\frac{{\mathrm{\&Sigma;m}}_{\mathrm{ij}}}{n},---\left(2\right)$

Described fractal cell S _ielement form matrix $F=\left(\begin{array}{ccc}{s}_{i1}& s_{i2}& s_{i3}\\ s_{i8}& 0& s_{i4}\\ s_{i7}& s_{i6}& s_{i5}\end{array}\right),$ If F will reach maximum information entropy, F should have each to the symmetry of digital density, and each w _ijvalue equate, make each s _ijp (s _ij) equate S _ishould meet (6) formula:

s _i1+s _i5＝s _i3+s _i7＝s _i4+s _i8＝s _i2+s _i6， (6)

So, S _ieach element be a solution of (7) formula:

Objective function max H (S _i) constraint condition:

$s.t.\left\{\begin{array}{c}{s}_{i1}+s_{i5}=s_{i3}+s_{i7}=s_{i4}+s_{i8}=s_{i2}+s_{i6},\\ s_{\mathrm{ij}}\&GreaterEqual;0,s_{\mathrm{ij}}\&Element;N\end{array}\right.---\left(7\right)$

Wherein, H (S _i) be the characteristic information entropy of structure, s _ijit is fractal cell S _ieach element value;

(7) the Xie Shi gang of formula separates, and chooses a solution from described family solution, execution step two;

Step 2, determine growth matrix, find the iterative manner of special cumulative structure, derive and obtain the growth matrix Y that i arbitrarily ties up special cumulative structural parameters ⁱ, the S calculating according to step 1 _iobtain the growth matrix that i ties up special cumulative structure;

Whether the parameter matrix of step 3, inspection institute's design meets the optimized requirement of special cumulative structural parameters matrix;

Step 4, determine parameter matrix, according to application, determine the parameter matrix of special cumulative structure, each element in parameter matrix is the parameter value of each unit of special cumulative structure, determine as required this parameter be area, volume, highly, strength of current, wave frequency or other required various physical quantitys, select, after physical quantity, to determine constant c, obtain the parameter matrix of designed structure;

Shape and the size of step 5, the material therefor that designs as required special cumulative structure, overall dimensions, shape and each structural unit.

The fractal cell matrix of special cumulative structure according to claim 1 and growth matrix production method, it is characterized in that, in step 3, the method for inspection of optimized the requirement whether parameter matrix of described inspection institute design meets special cumulative structural parameters matrix is as follows:

The condition that whether the growth matrix of design and parameter matrix meet special cumulative structure using following three conditions as inspection institute;

Condition (1): growth matrix has the described fractal characteristic of described step 1;

Condition (2): because the feature set of parameter matrix is obtained by formula (7), formula (7) has a plurality of solutions, so want the structural parameters matrix that inspection institute obtains whether to reach optimal value;

Definition matrix Y ⁱthe digital quality of each element be m _ij, Y ⁱtotal digital quality be G (Y ⁱ):

m _ij＝y _ij， (9)

$G\left(Y^i\right)=\underset{i,j}{\mathrm{\&Sigma;}}{m}_{\mathrm{ij}}=\underset{i,j}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}},---\left(10\right)$

Growth matrix Y ⁱthe digital barycenter of all elements at how much barycenter places of structure;

Condition (3): be to obtaining matrix after each element delivery 5 of growth matrix the digital barycenter of all elements is still at how much barycenter places of its structure;

If designed special cumulative structure reaches optimal value, S _i, Y ¹meet (7) formula and (8) formula, will meet above-mentioned condition (1), condition (2) and condition (3) simultaneously.

3. the production method of the fractal cell matrix of special cumulative structure according to claim 1 and growth matrix, is characterized in that, in step 2, the expression formula that described i ties up the growth matrix of special cumulative structure is:

$\begin{array}{c}{Y}^1={\left(\begin{array}{cccccccc}{y}_{11}& y_{12}& y_{13}& y_{14}& y_{15}& y_{16}& y_{17}& y_{18}\end{array}\right)}_{1\&times;8},(i=1),\\ Y^i={\left(\begin{array}{c}{s}_{i1}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i2}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i3}{E}_{(i-1)\&times;8}{+Y}^{i-1}\\ s_{i4}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i5}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i6}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i7}{E}_{(i-1)\&times;8}+Y^{i-1}\\ s_{i8}{E}_{(i-1)\&times;8}+Y^{i-1}\end{array}\right)}_{8^{i-1}\&times;8}\end{array}(i\&GreaterEqual;2),---\left(8\right)$

Y ⁱfor the i long matrix of supporting one's family, wherein: E _{i * j}that to tie up whole elements be 1 matrix to i * j; Y ¹requirement and the S of described step 1 _iidentical, Y ¹=(y ₁₁y ₁₂y ₁₃y ₁₄y ₁₅y ₁₆y ₁₇y ₁₈) _{1 * 8}for one-dimensional growth matrix, be called for short Y, wherein, s _ij, y _ijif ∈ N is the special cumulative structure of one dimension, Y required ¹=S _i, directly use the determined S of step 1 _i=(s _i1s _i2s _i3s _i4s _i5s _i6s _i7s _i8) _{1 * 8}; If designed is the above special cumulative structure of two dimension, by (8) formula, determine growth matrix.

4. the production method of the fractal cell matrix of special cumulative structure according to claim 1 and growth matrix, is characterized in that, in step 4, the expression formula of described parameter matrix is as follows:

X＝cY ⁱ， (11)

Wherein, c is plural number; The numerical value of each element of parameter matrix is for corresponding area physical quantity, volume physical quantity, degree of physical amount, wave frequency physical quantity, quantity of electric charge physical quantity and strength of current physical quantity.

The fractal cell matrix of special cumulative structure according to claim 1 and growth matrix production method, it is characterized in that, in step 1, the parameter matrix of described special cumulative structure has fractal characteristic, its fractal unit is that the mutually orthogonal and equal in length straight-line segment of two digital equal densities forms, the parameter matrix of special cumulative structure has fractal characteristic, and the affine variation of its two dimensional surface is:

$W\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}e\\ f\end{array}\right)=W\left(X\right)=A\left(X\right)+T,---\left(3\right)$

Wherein, $A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right),X=\left(\begin{array}{c}x\\ y\end{array}\right),T=\left(\begin{array}{c}e\\ f\end{array}\right);$

Convergent-divergent $A_1=\left(\begin{array}{cc}k& 0\\ 0& k\end{array}\right),$ Wherein, k is integer; Rotation $A_2=\left(\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right),\mathrm{\&theta;}=\frac{\mathrm{\&pi;}}{2}l.l\&Element;N,$ Translation $T=\left(\begin{array}{c}m\\ n\end{array}\right),m,n\&Element;N;$

If the feature set of the parameter matrix of special cumulative structure is: S _i=(s _i1s _i2s _i3s _i4s _i5s _i6s _i7s _i8) _{1 * 8}, wherein, s _ij∈ N, N is integer, element s _ijrepresent the feature classification of special cumulative structure, the characteristic information entropy of this structure is:

$H\left(T\right)=-\underset{j=1}{\overset{8}{\mathrm{\&Sigma;}}}p\left(s_{\mathrm{ij}}\right)\mathrm{lbp}\left(s_{\mathrm{ij}}\right),---\left(4\right)$

Wherein:

$p\left(s_{\mathrm{ij}}\right)=\frac{w_{\mathrm{ij}}n\left(s_{\mathrm{ij}}\right)}{\underset{j}{\mathrm{\&Sigma;}}{w}_{\mathrm{ij}}n\left(s_{\mathrm{ij}}\right)},---\left(5\right)$

Probability p (s _ij) be status flag s _ijat feature set S _ithe proportion of middle appearance, w _ijit is weighting coefficient.

6. the production method of the fractal cell matrix of special cumulative structure according to claim 5 and growth matrix, is characterized in that, the cavity effect of described special cumulative structure is only relevant with the ordering of each component units of structure.