An information compilation technology method based on the Julia fractal set

Abstract

The present invention relates to an information compilation technology method based on the Julia fractal set. The method includes the following steps: Step S1, information encoding: converting the input information into binary ASCII code and mapping it to complex numbers to generate a Julia set image with specific fractal features; Step S2, obtaining the fractal dimension D: obtaining the fractal dimension D of the fractal image through the box-counting method as the eigenvalue of the information; Step S3, information hiding and storage: storing the fractal image feature data and the fractal dimension D in a database to achieve dynamic storage of information; Step S4, information decoding and error correction: during the decoding process, obtaining the fractal dimension D of the fractal image, inversely deriving the original information based on this as an index, and using the fractal self-similarity to achieve error correction. The present invention can use the self-similarity and high complexity of the fractal image to achieve the concealment of information, the efficient compression of data, and the anti-interference ability.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to an information compilation technology method based on the Julia fractal set. Background Art

[0002] With the rapid development of information technologies such as AI, information security and data compression have become important research fields. Although traditional encryption technologies and data compression methods have solved these problems to a certain extent, there are still some limitations. For example, traditional encryption technologies are easily brute-forced, and traditional data compression methods are less efficient when dealing with complex data. Image compression technologies such as JPEG and PNG can achieve data compression, but when dealing with complex images, the compression efficiency is low and it is easy to lose detailed information, etc.

[0003] As a mathematical tool for describing complex structures in nature, the fractal theory has been widely applied in fields such as information coding, image processing, and data compression in recent years. Fractal images have self-similarity and high complexity, can effectively hide information, and have good anti-interference ability. Although there are already some image coding technologies based on the fractal theory, these technologies still have deficiencies in information hiding, data compression, and error correction ability. Therefore, the information coding technology based on the fractal theory has become an important research direction. Summary of the Invention

[0004] The purpose of the present invention is to provide an information compilation technology method based on the Julia fractal set, which can use the self-similarity and high complexity of fractal images to achieve information concealment, efficient data compression, and anti-interference ability.

[0005] To achieve the above purpose, the present invention provides the following technical solution: An information compilation technology method based on the Julia fractal set, the method includes the following steps:

[0006] Step S1, information encoding: Convert the input information into binary ASCII code and map it to complex numbers to generate a Julia set image with specific fractal features;

[0007] Step S2, obtaining the fractal dimension D1: Obtain the fractal dimension D1 of the fractal image by the box-counting method as the eigenvalue of the information;

[0008] Step S3, information hiding and storage: Store the fractal image feature data and the fractal dimension D1 in the database to achieve dynamic storage of information;

[0009] Step S4, information decoding and error correction: In the decoding process, obtain the fractal dimension D2 of the fractal image, reverse-derive the original information based on this as an index, and use fractal self-similarity to achieve error correction.

[0010] Further, the conversion of the input information into binary ASCII code in step S1 is further as follows:

[0011] Let the information bit sequence be , and the binary sequence corresponding to the generating polynomial be , where r is the order of the generating polynomial. For CRC8, r = 8;

[0012] Shift the information bits to the left by r positions to obtain , with r zeros at the back;

[0013] Then use and perform modulo-2 division. Start from the highest bit and make judgments bit by bit. If 's current highest bit is 1, then perform an exclusive OR operation with ; if it is 0, do not perform an operation, and then shift one bit to the left and continue the judgment for the next bit until 's number of bits is less than r. At this time, is the CRC8 checksum.

[0014] Further, the mapping of it to a complex number and generating a Julia set image with specific fractal characteristics in step S1 is further as follows: Map the binary ASCII code to a real number, which is used as the real part a in the complex number c = a + bi, and the imaginary part b is fixed at -0.2 to generate a Julia set image. Perform iterative calculations according to the value of the complex number c to generate a Julia set image, and generate a binary image through threshold processing.

[0015] Further, the Julia set image is further as follows:

[0016] 1) For a complex function , where is a complex number (x, y are real numbers, ), is also a complex number (a, b are real numbers);

[0017] 2) Starting from an initial complex number , iterate the function to obtain a sequence , where ;

[0018] 3) For a given c, define the Julia set as the set of all initial values for which the iterative sequence is bounded. Set.

[0019] Further, step S2 is further as follows: using a linear regression model to fit the relationship between the box size and the number of boxes on a logarithmic scale to obtain the fractal dimension D1. The steps are as follows:

[0020] 1) Determine a region containing the fractal set, such as a rectangular region;

[0021] 2) Select a series of different values, usually starting from a larger value and gradually decreasing;

[0022] 3) For each value, cover the fractal set with small squares or small cubes with side lengths, and count the number of required small squares or small cubes;

[0023] 4) Use as the ordinate and as the abscissa to plot a graph, and find the slope of the line through linear regression. This slope is the approximate value of the box dimension, that is, the fractal dimension D1.

[0024] Further, step S3 is further as follows: save the generated binary image in PNG format, and store the original string length, total number of bits, checksum, and fractal dimension D1 information in the image metadata; during the encoding process, each time data is encoded, the relevant information is stored in the database; use the Pandas library to read and process Excel files to facilitate database management.

[0025] Further, during the decoding process in step S4, to obtain the fractal dimension D2 of the fractal image and reverse-derive the original information based on this as the index: read the fractal image to be decoded and extract its metadata; after converting the image to a binary image, obtain its fractal dimension D2; in the `read_database` function, read data from the database and construct an index, and find the entry closest to the current fractal dimension D2 through the `find_closest_entry` function. Then, use the `real_to_input_parallel` function to reverse-index the real part of the complex number c in the database through a parallel search strategy of dynamic range and priority blocks, combined with metadata information, and then reverse-derive the ASCII code, and finally restore the original input characters;

[0026] When the imaginary part b in the complex number c = a + bi is fixed at 0, that is, c = a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation , such that is a cubic polynomial on each subinterval , and satisfies:

[0027] 1) , i = 0, 1…n, that is, the spline function takes the same values at the given data points as the original data;

[0028] 2) has continuous first-order and second-order derivatives over the entire interval ;

[0029] This can directly achieve the direct mapping from the fractal dimension D2 to the real part of the C value. However, when the imaginary part of the C value is not 0, the data heterogeneity is too strong, so the data mapping is achieved by means of dynamic database retrieval and matching.

[0030] Furthermore, the error correction by using fractal self-similarity in step S4 is further as follows: Ridge regression is adopted, and the regularization parameter, that is, the alpha value is set to 0.001, to obtain the relationship between the local and the whole of the fractal code symbol carrier. The box-counting method is used to calculate the fractal dimension value for the undamaged local area of the fractal code, and multiple local fractal dimension values are obtained; through a large amount of experimental data or theoretical analysis, the mapping relationship between the local fractal dimension value and the whole fractal dimension value is established. The extracted local fractal dimension value is substituted into the mapping relationship to calculate the whole fractal dimension value, and then it is compared with the pre-stored standard fractal dimension value; if the difference is within the allowable error range, error correction operations are performed according to the difference; if the difference is too large, it is determined that error correction cannot be performed.

[0031] Furthermore, the parallel search strategy in step S4 is further as follows: The adaptive block dynamic search algorithm is adopted, and the search strategy is dynamically adjusted according to the data range and block size. Through the parallel search algorithm, the original information is inversely deduced according to the real part of the complex number c, the length of the original string, the total number of bits and the checksum, and the checksum verification is performed.

[0032] Advantages of the present invention:

[0033] 1. Data hiding and security

[0034] Data encryption feature: Fractal coding converts the input string into a Julia set image, and this coding method has a certain degree of concealment. Due to the complexity of the image itself, it is very difficult for outsiders to directly extract the original coding information from the image, which is equivalent to encrypting the data to a certain extent and enhancing the security of the data.

[0035] Difficult to crack: Encoding and decoding are carried out through complex mathematical features such as fractal dimension, which increases the difficulty of cracking. For attackers who do not master the decoding algorithm and related parameters, it is very difficult to restore the original data from the image.

[0036] 2. Data storage and transmission

[0037] Stored in the form of an image: The data is stored in the form of an image. Compared with the traditional text storage method, it may be easier to store and manage in some scenarios. For example, images can be conveniently stored and retrieved in various image databases or file systems.

[0038] Potential compression advantage: Fractal coding can achieve effective compression of data in some cases. By mapping the data into a fractal image, the storage space requirement of the data may be reduced, especially for some data with repetitiveness or self-similarity.

[0039] 3. Scalability

[0040] Multi-field applications: Fractal coding and decoding systems can be applied to multiple fields, such as data hiding, image watermarking, digital copyright protection, etc. The parameters and algorithms of encoding and decoding can be adjusted according to different application requirements, with strong scalability.

[0041] The present invention realizes the concealment of information, the efficient compression of data and the anti-interference ability through the information coding technology based on fractal theory. Through the self-similarity and high complexity of the fractal image, the present invention has broad application prospects in the fields of information security, data compression and digital watermarking. In the future, the present invention will further optimize the fractal dimension calculation algorithm, enhance the security of information, and explore applications in more fields. Description of the Drawings

[0042] Figure 1 It is a schematic flow chart of the encoding process of the present invention;

[0043] Figure 2 It is a schematic flow chart of the decoding process of the present invention;

[0044] Figure 3 It is an example diagram of the Julia set carrier of the present invention;

[0045] Figure 4 The self-similarity example diagram of the part and the whole of the present invention;

[0046] Figure 5 It is a Julia set diagram of the present invention;

[0047] Figure 6 It is an encoding interface diagram of the present invention;

[0048] Figure 7 It is a decoding interface diagram of the present invention. Detailed Embodiments

[0049] The following further describes the present invention with reference to the drawings.

[0050] Please refer to Figures 1 to 7 , the present invention provides an embodiment:

[0051] An information compilation technology method based on the Julia fractal set, the method comprising the following steps:

[0052] Step S1, Information Encoding: Convert the input information into binary ASCII code, map it to complex numbers, and generate a Julia set image with specific fractal features;

[0053] Step S2, Obtain Fractal Dimension D1: Obtain the fractal dimension D1 of the fractal image through the box-counting method as the eigenvalue of the information;

[0054] Step S3, Information Hiding and Storage: Store the fractal image feature data and the fractal dimension D1 in the database to achieve dynamic storage of information;

[0055] Step S4, Information Decoding and Error Correction: During the decoding process, obtain the fractal dimension D2 of the fractal image, reverse-derive the original information based on this as an index, and use the fractal self-similarity to achieve error correction.

[0056] The following further illustrates the present invention in conjunction with a specific embodiment:

[0057] An information compilation technology method based on the Julia fractal set,

[0058] Step S1, Information Encoding: Convert the input information into binary ASCII code, map it to complex numbers, and generate a Julia set image with specific fractal features; The input information currently mainly realizes the combination of 0 - 9, 26 uppercase and lowercase English letters. Convert the input information into binary ASCII code and calculate the CRC8 checksum to ensure the integrity of the information. Among them, the ASCII (American Standard Code for Information Interchange) code is a set of computer coding systems based on the Latin alphabet. In the ASCII code table, the decimal ASCII code values corresponding to the numbers 0 - 9 are 48 - 57 respectively, the decimal ASCII code values corresponding to the uppercase letters A - Z are 65 - 90, and the decimal ASCII code values corresponding to the lowercase letters a - z are 97 - 122. To convert the decimal ASCII code value to binary, the method of dividing by 2 and taking the remainder can be used to convert the decimal ASCII code value into binary. CRC (Cyclic Redundancy Check) is a cyclic redundancy check code used to detect errors during data transmission. CRC8 is one of them, and the checksum it generates is 8 bits.

[0059] The conversion of the input information into binary ASCII code in Step S1 is further as follows:

[0060] Let the information bit sequence be The binary sequence corresponding to the generating polynomial is r is the order of the generating polynomial. For CRC8, r = 8;

[0061] Shift the information bits to the left by r positions to obtain , followed by r zeros;

[0062] Then use and to perform modulo 2 division (actually XOR operation). Starting from the highest bit, make judgments bit by bit. If 's current highest bit is 1, then perform an XOR operation with ; if it is 0, no operation is performed. Then shift one bit to the left and continue to judge the next bit until 's number of bits is less than r. At this time, is the CRC8 checksum.

[0063] Map it to a complex number and generate a Julia set image with specific fractal characteristics. Further, map the binary ASCII code to a real number, which is used as the real part a in the complex number c = a + bi, and the imaginary part b is fixed at -0.2 to generate a Julia set image. Perform iterative calculations based on the value of the complex number c to generate a Julia set image, and generate a binary image through threshold processing.

[0064] The said Julia set image is further as follows:

[0065] 1) For a complex function , where is a complex number (x, y are real numbers, ), is also a complex number (a, b are real numbers);

[0066] 2) Starting from an initial complex number , iterate the function to obtain a sequence , where ;

[0067] 3) For a given c, define the Julia set as the set of all initial values for which the iterative sequence is bounded. Set. It has been verified that for the Julia set, the real and imaginary parts of the complex number c have strong fractal spatial heterogeneity within the above value range, which can ensure sufficient diversity of data carriers when the amount of information is large. Perform iterative calculations based on the value of the complex number c to generate a Julia set image, and generate a binary image through threshold processing. As shown Figure 3 below.

[0068] Step S2. Obtain the fractal dimension D1: Obtain the fractal dimension D1 of the fractal image through the box-counting method as the eigenvalue of the information;

[0069] Further, step S2 is further as follows: Use a linear regression model to fit the relationship between the box size and the number of boxes on a logarithmic scale to obtain the fractal dimension D1. The steps are as follows:

[0070] 1) Determine a region containing the fractal set, such as a rectangular region;

[0071] 2) Select a series of different values, usually starting from a larger value and gradually decreasing;

[0072] 3) For each value, cover the fractal set with small squares or small cubes with side lengths, and count the number of required small squares or small cubes;

[0073] 4) Use as the ordinate and as the abscissa to plot a graph, and find the slope of the line through methods such as linear regression. This slope is the approximate value of the box dimension, that is, the fractal dimension D1.

[0074] Step S3. Information hiding and storage: Store the fractal image feature data and the fractal dimension D1 in the database to achieve dynamic storage of information;

[0075] Further: Save the generated binary image in PNG format, and store information such as the original string length, total number of bits, checksum, and fractal dimension D1 in the image metadata; during the encoding process, store the relevant information in the database every time data is encoded; use the Pandas library to read and process Excel files to facilitate database management.

[0076] Step S4. Information decoding and error correction: During the decoding process, obtain the fractal dimension D2 of the fractal image, reverse-derive the original information based on this as an index, and use the fractal self-similarity to achieve error correction.

[0077] Using the fractal self-similarity to achieve error correction is further as follows: Adopt ridge regression, set the regularization parameter, that is, the alpha value is 0.001, to obtain the relationship between the local and the whole of the fractal code symbol carrier. Use the box-counting method to calculate the fractal value for the undamaged local area of the fractal code to obtain multiple local fractal values; through a large amount of experimental data or theoretical analysis, establish the mapping relationship between the local fractal value and the whole fractal value. Substitute the extracted local fractal value into the mapping relationship to calculate the whole fractal value, and then compare it with the pre-stored standard fractal value; if the difference is within the allowable error range, perform error correction operations according to the difference; if the difference is too large, it is determined that error correction cannot be performed.

[0078] During the decoding process, the fractal dimension D2 of the fractal image is obtained, and the original information is deduced backward using this as an index. Further steps are as follows: Read the fractal image to be decoded and extract its metadata (including the original string length, total number of bits, checksum, etc.); After converting the image into a binary image, obtain its fractal dimension D2; In the `read_database` function, read data from the database and build an index, and use the `find_closest_entry` function to find the entry closest to the current fractal dimension D2. Then, use the `real_to_input_parallel` function to reverse-index the real part of the complex number c in the database through a parallel search strategy of dynamic range and priority chunking, combined with the metadata information, and then reverse-deduce the ASCII code, and finally restore the original input characters;

[0079] When the imaginary part b in the complex number c = a + bi is fixed at 0, that is, c = a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation , such that On each sub-interval is a cubic polynomial and satisfies:

[0080] 1) , i = 0, 1…n, that is, the spline function takes the same value as the original data at the given data points;

[0081] 2) On the entire interval has continuous first and second derivatives;

[0082] This can directly achieve the direct mapping from the fractal dimension D to the real part of the C value. However, when the imaginary part of the C value is not 0, the data heterogeneity is too strong, so a dynamic database retrieval and matching method is used to achieve data mapping.

[0083] Among them, in steps S1 and S2, when generating the julia image, the fractal dimension is calculated and stored in the database. At this time, the fractal dimension D1 is calculated based on the image digital matrix (i.e., the 0, 1 matrix). When decoding in step S4, the fractal dimension value D2 is calculated based on the binary image of the image. The calculation methods used by both are the same, but there may be differences in the results due to the different presentation forms of the calculation objects. Therefore, there is a corresponding pairing review mechanism during database indexing.

[0084] The parallel search strategy is further as follows: The adaptive block dynamic search algorithm is adopted to dynamically adjust the search strategy according to the data range and block size. Through the parallel search algorithm, based on the real part of the complex number c, the length of the original string, the total number of bits, and the checksum, the original information is deduced reversely and the checksum verification is carried out. During the encoding and decoding processes, the CRC8 algorithm is used to calculate the checksum of the input string. In the `calculate_checksum` function, the checksum of the input information is calculated and stored in the image metadata or database. During decoding, the checksum is recalculated and compared with the stored checksum. If the two are consistent, it indicates that the information has not been tampered with during transmission and storage, ensuring the integrity and accuracy of the data.

[0085] Through the self-similarity of the fractal image, that is, locally and globally having geometric or statistical self-similarity within a specific interval range (scale-free region), such as Figure 4 As shown, the regions marked by the frames have obvious geometric similarity from small to large. Utilizing the self-similarity of the fractal image, the overall fractal dimension value is deduced from the local fractal dimension values to achieve information error correction. First, the box-counting method is used to calculate the fractal dimension values for the local regions where the fractal dimension codes are not damaged, obtaining multiple local fractal dimension values. Through a large amount of experimental data or theoretical analysis, a mapping relationship between the local fractal dimension values and the overall fractal dimension value is established. The extracted local fractal dimension values are substituted into the mapping relationship to deduce the overall fractal dimension value, which is then compared with the pre-stored standard fractal dimension value. If the difference is within the allowable error range, error correction operations are performed according to the difference; if the difference is too large, it is determined that error correction cannot be carried out. This error correction method makes full use of the self-similar characteristics of the fractal body, does not require additional addition of a large amount of redundant information, improves the information utilization rate, and enhances the anti-interference ability and adaptability of the fractal dimension code to a certain extent.

[0086] The above are only the preferred embodiments of the present invention and should not be construed as limitations to this application. All equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by the present invention.

Claims

1. An information compilation technology method based on the Julia fractal set, characterized in that: The method includes the following steps: Step S1, Information Encoding: Convert the input information into binary ASCII code and map it to complex numbers to generate a Julia set image with specific fractal features; Step S2, Obtain the Fractal Dimension D: Obtain the fractal dimension D1 of the fractal image through the box-counting method as the eigenvalue of the information; Step S3, Information Hiding and Storage: Store the fractal image feature data and the fractal dimension D1 in the database to achieve dynamic storage of information; Step S4, Information Decoding and Error Correction: During the decoding process, obtain the fractal dimension D2 of the fractal image, reverse-derive the original information based on this as an index, and use the fractal self-similarity to achieve error correction; The use of fractal self-similarity to achieve error correction in step S4 is further as follows: Adopt ridge regression, set the regularization parameter, that is, the alpha value is 0.001, obtain the relationship between the local and the whole of the fractal code symbol carrier, calculate the fractal dimension value for the undamaged local area of the fractal code using the box-counting method to obtain multiple local fractal dimension values; Through a large number of experimental data or theoretical analysis, establish the mapping relationship between the local fractal dimension values and the whole fractal dimension value; Substitute the extracted local fractal dimension values into the mapping relationship to deduce the whole fractal dimension value, and then compare it with the pre-stored standard fractal dimension value; If the difference is within the allowable error range, perform error correction operations according to the difference; If the difference is too large, it is determined that error correction cannot be performed; During the decoding process in step S4, obtaining the fractal dimension D2 of the fractal image and reverse-deriving the original information based on this as an index is further as follows: Read the fractal image to be decoded and extract its metadata; After converting the image into a binary image, obtain its fractal dimension D2; In the `read_database` function, read data from the database and construct an index, find the entry closest to the current fractal dimension D2 through the `find_closest_entry` function, and then, using the `real_to_input_parallel` function, through the parallel search strategy of dynamic range and priority block, combined with the metadata information, reverse-index the real part of the complex number c in the database, and then reverse-deduce the ASCII code, and finally restore the original input character; When the imaginary part b in the complex number c = a + bi is fixed at 0, that is, c = a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation. , such that is a cubic polynomial on each subinterval and satisfies: 1) , where \(i = 0, 1, \ldots, n\), that is, the spline function takes the same values as the original data at the given data points; 2) has continuous first and second derivatives over the entire interval In this way, a direct mapping from the fractal dimension D2 to the real part of the C value can be directly achieved, but when the imaginary part of the C value is not 0, the data heterogeneity is too strong, and the data mapping is achieved by using the dynamic database retrieval and matching method.

2. The information compilation technology method based on the Julia fractal set according to claim 1, characterized in that: The conversion of the input information into binary ASCII code in step S1 is further as follows: Let the information bit sequence be , and the binary sequence corresponding to the generating polynomial be . Let r be the order of the generating polynomial. For CRC8, r = 8; Shift the information bits r positions to the left to obtain , followed by r zeros; Then use and to perform modulo-2 division. Start from the highest bit and make judgments bit by bit. If 's current highest bit is 1, then perform an exclusive OR operation with ; if it is 0, do not perform an operation. Then shift one bit to the left and continue to make judgments for the next bit until 's number of bits is less than r. At this time, is the CRC8 checksum.

3. The information compilation technology method based on the Julia fractal set according to claim 1 is characterized in that: Mapping it to a complex number in step S1 to generate a Julia set image with specific fractal characteristics is further as follows: mapping binary ASCII codes to real numbers, taking them as the real part a in the complex number c = a + bi, and fixing the imaginary part b as -0.2 to generate a Julia set with specific fractal characteristics. For the image, iterative calculations are performed according to the value of the complex number c to generate a Julia set image, and a binary image is generated through threshold processing.

4. A method for information compilation technology based on the Julia fractal set according to claim 3, characterized in that: The Julia set The image is further as follows: 1) For a complex function , where is a complex number, x and y are real numbers, , is also a complex number, and a and b are real numbers; 2) Starting from an initial complex number and iterating the function , a sequence is obtained, where ; 3) For a given c, define the Julia set as the set of all initial values for which the iteration sequence is bounded. Set.

5. A method for information compilation technology based on the Julia fractal set according to claim 1, characterized in that: Step S2 is further as follows. Use a linear regression model to fit the relationship between the box size and the number of boxes on a logarithmic scale to obtain the fractal dimension D1. The steps are as follows: 1) Determine a region that contains the fractal set, and this region is a rectangular region; 2) Select a series of different values, usually starting from a larger value and gradually decreasing; 3) For each value, use small squares or small cubes with side lengths to cover the fractal set, and count the number of required small squares or small cubes; 4) Taking as the ordinate and as the abscissa, plot a graph, and find the slope of the straight line through the linear regression method. This slope is the approximate value of the box dimension, that is, the fractal dimension D1.

6. A method for information compilation technology based on the Julia fractal set according to claim 1, characterized in that: The step S3 is further as follows: Save the generated binary image in PNG format, and store the original string length, total number of bits, checksum, and fractal dimension D1 information in the image metadata; during the encoding process, every time data is encoded, the relevant information is stored in the database; use the Pandas library to read and process Excel files to facilitate the management of the database.

7. A method for information compilation technology based on the Julia fractal set according to claim 1, characterized in that: The parallel search strategy of the step S4 is further as follows: Adopt an adaptive block dynamic search algorithm, dynamically adjust the search strategy according to the data range and block size, and through the parallel search algorithm, reverse-derive the original information based on the real part of the complex number c, the original string length, the total number of bits, and the checksum, and perform checksum verification.

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