Information compiling technical method based on Julia fractal set

Abstract

The invention relates to an information compiling technical method based on a Julia fractal set, and the method comprises the following steps: S1, information coding: converting input information into a binary ASCII code, mapping the binary ASCII code into a complex number, and generating a Julia set image with a specific fractal feature; s2, obtaining a fractal dimension D: obtaining the fractal dimension D of the fractal image through a box counting method, and taking the fractal dimension D as a feature value of the information; s3, information hiding and storage: storing the fractal image feature data and the fractal dimension D in a database to realize dynamic storage of the information; and S4, information decoding and error correction: in the decoding process, obtaining the fractal dimension D of the fractal image, reversely deriving original information by taking the fractal dimension D as an index, and realizing error correction by utilizing fractal self-similarity. According to the method, the concealment of information, the efficient compression of data and the anti-interference capability can be realized by using the self-similarity and the high complexity of the fractal image.

Description

Technical Field

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

[0002] With the rapid development of information technology such as AI, information security and data compression have become important research areas. Although traditional encryption technology and data compression methods have solved these problems to a certain extent, they still have some limitations. For example, traditional encryption technology is easily cracked by brute force, and traditional data compression methods are inefficient when processing complex data. Image compression technologies such as JPEG and PNG can achieve data compression, but when processing complex images, the compression efficiency is low and it is easy to lose detailed information.

[0003] As a mathematical tool to describe the complex structure of nature, fractal theory has been widely used in information coding, image processing and data compression in recent years. Fractal images are self-similar and highly complex, can effectively hide information, and have good anti-interference ability. Although there are some image coding technologies based on fractal theory, these technologies still have shortcomings in information hiding, data compression and error correction capabilities. Therefore, information coding technology based on 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 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 object, the present invention provides the following technical solution: an information compilation method based on Julia fractal set, the method comprising the following steps: Step S1, information encoding: converting the input information into binary ASCII code and mapping it into complex numbers to generate a Julia set image with specific fractal features; Step S2, obtaining the fractal dimension D1: obtaining the fractal dimension D1 of the fractal image by a box counting method as a characteristic value of the information; Step S3, information hiding and storage: storing the fractal image feature data and fractal dimension D1 in a database to achieve dynamic storage of information; Step S4, information decoding and error correction: During the decoding process, the fractal dimension D2 of the fractal image is obtained, which is used as an index to reversely deduce the original information, and error correction is achieved using fractal self-similarity.

[0006] Furthermore, the step S1 of converting the input information into binary ASCII code is further as follows: Assume the information bit sequence is , the binary sequence corresponding to the generating polynomial is , r is the order of the generating polynomial, for CRC8, r=8; Shift the information bit left by r, and we get , followed by r zeros; Then use And perform modulo 2 division, starting from the high bit, judge bit by bit. If The current highest bit of is 1, then Perform an XOR operation; if it is 0, no operation is performed, and then Shift one bit to the left and continue to judge the next bit until The number of digits is less than r, then It is the CRC8 checksum.

[0007] Furthermore, the step S1 of mapping it into a complex number to generate a Julia set image with specific fractal features is further as follows: mapping the binary ASCII code into a real number, as the real part a in the complex number c=a+bi, and the imaginary part b is fixed to -0.2, to generate a Julia set with specific fractal features The image is iteratively calculated according to the value of the complex number c to generate the Julia set image, and the binary image is generated through threshold processing.

[0008] Furthermore, the Julia set The image is further: 1) For a complex function ,in is a complex number (x, y are real numbers, ), is also a complex number (a, b are real numbers); 2) From an initial plural To begin, for the function Iterate and get a sequence ,in ; 3) For a given c, define the Julia set For all such that the iterative sequence Bounded initial value gather.

[0009] Furthermore, the step S2 is further to use a linear regression model to fit the relationship between the box size and the number of boxes in a logarithmic scale to obtain the fractal dimension D1, the steps are as follows: 1) Determine an area containing the fractal set, such as a rectangular area; 2) Choose a range of different values, usually starting with a larger value and gradually decreasing; 3) For each value, use small squares or cubes with a side length of to cover the fractal set, and count the number of small squares or cubes required; 4) Plot a graph with as the ordinate and as the abscissa, and use linear regression method to find the slope of the straight line. The slope is the approximate value of the box dimension, that is, the fractal dimension D1.

[0010] Furthermore, the step S3 is further as follows: saving the generated binary image in PNG format, and storing 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; using the Pandas library to read and process Excel files to facilitate the management of the database.

[0011] Furthermore, in the decoding process of step S4, the fractal dimension D2 of the fractal image is obtained, and the original information is reversely deduced based on this as an index. The fractal image to be decoded is read and its metadata is extracted; after the image is converted into a binary image, its fractal dimension D2 is obtained; in the `read_database` function, data is read from the database and an index is constructed, and the entry closest to the current fractal dimension D2 is found through the `find_closest_entry` function. Then, the `real_to_input_parallel` function is used to reversely 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 the ASCII code is reversed to finally restore the original input character; When the imaginary part b in the complex number c=a+bi is fixed to 0, that is, c=a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation ,make In each subinterval [ ] is a cubic polynomial and satisfies: 1) , i=0,1…n, that is, the value of the spline function at a given data point is the same as the original data; 2) In the whole range has continuous first-order and second-order derivatives; In this way, the direct mapping of the fractal dimension D2 to the real part of the C value can be directly realized. However, when the imaginary part of the C value is not 0, the data heterogeneity is too strong, and the data mapping is realized by dynamic database retrieval matching.

[0012] Furthermore, the error correction using fractal self-similarity in step S4 is further as follows: using ridge regression, setting the regularization parameter, that is, the alpha value is 0.001, obtaining the local and overall relationship between the fractal code symbol carrier, using the box counting method to calculate the fractal dimension value of the undamaged local area of ​​the fractal code, and obtaining multiple local fractal dimension values; through a large amount of experimental data or theoretical analysis, a mapping relationship between the local fractal dimension value and the overall fractal dimension value is established. Substitute the extracted local fractal dimension value into the mapping relationship, deduce the overall 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 an error correction operation based on the difference; if the difference is too large, it is determined that the error cannot be corrected.

[0013] Furthermore, the parallel search strategy of step S4 is further as follows: an adaptive block dynamic search algorithm is adopted to dynamically adjust the search strategy according to the data range and block size, and the original information is reversely derived through the parallel search algorithm according to the real part of the complex number c, the original string length, the total number of bits and the checksum, and then checked and verified.

[0014] Beneficial effects of the present invention: 1. Data hiding and security Data encryption characteristics: Fractal coding converts the input string into a Julia set image. This encoding method has a certain degree of concealment. Due to the complexity of the image itself, it is difficult for outsiders to directly extract the original encoding information from the image. It is equivalent to encrypting the data, which enhances the security of the data.

[0015] Difficult to crack: Encoding and decoding through complex mathematical features such as fractal dimension increases the difficulty of cracking. For attackers who do not understand the decoding algorithm and related parameters, it is difficult to restore the original data from the image.

[0016] 2. Data storage and transmission Image storage: Storing data in the form of images may be easier to store and manage than traditional text storage in some scenarios. For example, images can be easily stored and retrieved in various image databases or file systems.

[0017] Potential compression advantages: Fractal coding can achieve effective data compression in some cases. By mapping data into fractal images, the storage space requirements of the data may be reduced, especially for some repetitive or self-similar data.

[0018] 3. Scalability Multi-field application: Fractal encoding and decoding systems can be applied to multiple fields, such as data hiding, image watermarking, digital copyright protection, etc. The encoding and decoding parameters and algorithms can be adjusted according to different application requirements, and it has strong scalability.

[0019] The present invention realizes the concealment of information, efficient data compression and anti-interference ability through information coding technology based on fractal theory. Through the self-similarity and high complexity of fractal images, 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the flow of the encoding process of the present invention; Figure 2 It is a flowchart of the decoding process of the present invention; Figure 3 This is an example diagram of the Julia set vector of the present invention; Figure 4 Example diagram of the self-similarity of the local and the whole of the present invention; Figure 5 It is the Julia set diagram of the present invention; Figure 6 This is the coding interface diagram of the present invention; Figure 7 This is a decoding interface diagram of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described below in conjunction with the accompanying drawings.

[0022] See also Figures 1 to 7 , the present invention provides an embodiment: An information compilation technology method based on Julia fractal set, the method comprising the following steps: Step S1, information encoding: converting the input information into binary ASCII code and mapping it into complex numbers to generate a Julia set image with specific fractal features; Step S2, obtaining the fractal dimension D1: obtaining the fractal dimension D1 of the fractal image by a box counting method as a characteristic value of the information; Step S3, information hiding and storage: storing the fractal image feature data and fractal dimension D1 in a database to achieve dynamic storage of information; Step S4, information decoding and error correction: During the decoding process, the fractal dimension D2 of the fractal image is obtained, which is used as an index to reversely deduce the original information, and error correction is achieved using fractal self-similarity.

[0023] The present invention will be further described below in conjunction with a specific embodiment: A method of information compilation technology based on Julia fractal set, Step S1, information encoding: convert the input information into binary ASCII code, and map it into a complex number to generate a Julia set image with specific fractal features; the input information currently mainly realizes the combination of uppercase and lowercase letters 0-9 and 26 English letters, converts the input information into binary ASCII code, and calculates the CRC8 checksum to ensure the integrity of the information. Among them, the ASCII (American Standard Code for Information Interchange) code is a computer encoding system based on the Latin alphabet. In the ASCII code table, the decimal ASCII code values ​​corresponding to the numbers 0-9 are 48-57, 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. The decimal ASCII code value is converted to binary, and the decimal ASCII code value can be converted to binary using the method of dividing by 2 and taking the remainder. CRC (Cyclic Redundancy Check) is a cyclic redundancy check code used to detect errors in the data transmission process. CRC8 is one of them, and the checksum it generates is 8 bits.

[0024] The step S1 of converting the input information into binary ASCII code is further as follows: Assume the information bit sequence is , the binary sequence corresponding to the generating polynomial is , r is the order of the generating polynomial, for CRC8, r=8; Shift the information bit left by r, and we get , followed by r zeros; Then use and Perform modulo 2 division (actually XOR operation), and judge bit by bit starting from the high bit. If The current highest bit of is 1, then Perform an XOR operation; if it is 0, no operation is performed, and then Shift one bit to the left and continue to judge the next bit until The number of digits is less than r, then It is the CRC8 checksum.

[0025] Map it to complex numbers to generate a Julia set with specific fractal characteristics. The image is further: map the binary ASCII code to real numbers, as the real part a in the complex number c=a+bi, and the imaginary part b is fixed to -0.2, to generate a Julia set with specific fractal characteristics. The image is iteratively calculated according to the value of the complex number c to generate the Julia set image, and the binary image is generated through threshold processing.

[0026] The Julia set The image is further: 1) For a complex function ,in is a complex number (x, y are real numbers, ), is also a complex number (a, b are real numbers); 2) From an initial plural To begin, for the function Iterate and get a sequence ,in ; 3) For a given c, define the Julia set For all such that the iterative sequence Bounded initial value It has been verified that for Julia sets, the real and imaginary parts of the complex number c have strong fractal spatial heterogeneity within the above range of values, which can ensure that the diversity of data carriers is sufficient when the amount of information is large. Iterative calculations are performed based on the values ​​of the complex number c to generate the Julia set image, and a binary image is generated through threshold processing. Figure 3 shown.

[0027] Step S2, obtaining the fractal dimension D1: obtaining the fractal dimension D1 of the fractal image by a box counting method as a characteristic value of the information; Furthermore, the step S2 is further to use a linear regression model to fit the relationship between the box size and the number of boxes in a logarithmic scale to obtain the fractal dimension D1, the steps are as follows: 1) Determine an area containing the fractal set, such as a rectangular area; 2) Choose a range of different values, usually starting with a larger value and gradually decreasing; 3) For each value, use small squares or cubes with a side length of to cover the fractal set, and count the number of small squares or cubes required; 4) Plot a graph with as the ordinate and as the abscissa, and find the slope of the line through linear regression and other methods. The slope is the approximate value of the box dimension, that is, the fractal dimension D1.

[0028] Step S3, information hiding and storage: storing the fractal image feature data and fractal dimension D1 in a database to achieve dynamic storage of information; Further steps include: saving the generated binary image in PNG format, and storing information such as the original string length, total number of bits, checksum, fractal dimension D1, etc. in the image metadata; during the encoding process, each time data is encoded, the relevant information is stored in the database; using the Pandas library to read and process Excel files, it is convenient to manage the database.

[0029] Step S4, information decoding and error correction: During the decoding process, the fractal dimension D2 of the fractal image is obtained, which is used as an index to reversely deduce the original information, and error correction is achieved using fractal self-similarity.

[0030] The error correction using fractal self-similarity is further implemented as follows: using ridge regression, setting the regularization parameter, that is, the alpha value is 0.001, obtaining the local and overall relationship between the fractal code symbol carrier, using the box counting method to calculate the fractal dimension value of the undamaged local area of ​​the fractal code, and obtaining multiple local fractal dimension values; through a large amount of experimental data or theoretical analysis, a mapping relationship between the local fractal dimension value and the overall fractal dimension value is established. Substitute the extracted local fractal dimension value into the mapping relationship, calculate the overall 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 an error correction operation based on the difference; if the difference is too large, it is determined that the error cannot be corrected.

[0031] During the decoding process, the fractal dimension D2 of the fractal image is obtained, and the original information is reversely deduced based on this as an index. The following steps are performed: read the fractal image to be decoded, extract its metadata (including the original string length, total number of bits, checksum, etc.); convert the image into a binary image, and 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, using the `real_to_input_parallel` function, through the parallel search strategy of dynamic range and priority block, combined with metadata information, reverse index the real part of the complex number c in the database, and then reversely 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 to 0, that is, c=a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation. ,make In each subinterval [ ] is a cubic polynomial and satisfies: 1) , i=0,1…n, that is, the value of the spline function at a given data point is the same as the original data; 2) In the whole range has continuous first-order and second-order derivatives; In this way, the direct mapping of the fractal dimension D to the real part of the C value can be directly realized. However, when the imaginary part of the C value is not 0, the data heterogeneity is too strong, and the data mapping is realized by dynamic database retrieval matching.

[0032] Among them, in steps S1 and S2, when the Julia image is generated, the fractal dimension will be calculated and stored in the database. At this time, the fractal dimension D1 is calculated based on the image digital matrix (that is, the 0, 1 matrix), and during decoding in step S4, the fractal dimension value D2 is calculated based on the binary image of the image. The calculation method used in the two is the same, but due to the different presentation forms of the calculation objects, there may be differences in the results, so there is a corresponding pairing review mechanism when indexing the database.

[0033] The parallel search strategy is further as follows: an adaptive block dynamic search algorithm is used to dynamically adjust the search strategy according to the data range and block size. Through the parallel search algorithm, the original information is reversely derived according to the real part of the complex number c, the original string length, the total number of bits and the checksum, and the checksum is verified. In both 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 means that the information has not been tampered with during transmission and storage, ensuring the integrity and accuracy of the data.

[0034] Through the self-similarity of fractal images, that is, within a specific range (scale-free area), the local and the whole have geometric or statistical self-similarities, such as Figure 4 As shown in the figure, the area marked by the box has obvious geometric similarity from small to large. By using the self-similarity of the fractal image, the overall fractal dimension value is inferred by the local partial dimension value to realize the error correction of information. First, the fractal dimension value is calculated by the box counting method for the local area where the fractal code is not damaged, and multiple local partial dimension values ​​are obtained. Through a large amount of experimental data or theoretical analysis, a mapping relationship between the local partial dimension value and the overall fractal dimension value is established. The extracted local partial dimension value is substituted into the mapping relationship, the overall fractal dimension value is inferred, and then compared with the pre-stored standard fractal dimension value. If the difference is within the allowable error range, the error correction operation is performed according to the difference; if the difference is too large, it is determined that the error cannot be corrected. This error correction method makes full use of the self-similarity characteristics of the fractal body, does not need to add a large amount of redundant information, improves the information utilization rate, and enhances the anti-interference ability and adaptability of the fractal code to a certain extent.

[0035] The above description is only a preferred embodiment of the present invention and should not be construed as limiting the present application. All equivalent changes and modifications made within the scope of the patent application of the present invention should fall within the scope of the present invention.

Claims

1. An information compilation technology method based on Julia fractal set, characterized by: The method comprises the following steps: Step S1, information encoding: converting the input information into binary ASCII code and mapping it into complex numbers to generate a Julia set image with specific fractal features; Step S2, obtaining fractal dimension D: obtaining fractal dimension D1 of the fractal image by box counting method as a characteristic value of the information; Step S3, information hiding and storage: storing the fractal image feature data and fractal dimension D1 in a database to achieve dynamic storage of information; Step S4, information decoding and error correction: During the decoding process, the fractal dimension D2 of the fractal image is obtained, which is used as an index to reversely deduce the original information, and error correction is achieved using fractal self-similarity.

2. The information compilation technology method based on Julia fractal set according to claim 1, characterized in that: The step S1 of converting the input information into binary ASCII code is further as follows: Assume the information bit sequence is , the binary sequence corresponding to the generating polynomial is , r is the order of the generating polynomial, for CRC8, r=8; Shift the information bit left by r, and we get , followed by r zeros; Then use and Perform modulo 2 division, starting from the high bit and judging bit by bit. If The current highest bit of is 1, then Perform an XOR operation; if it is 0, no operation is performed, and then Shift one bit to the left and continue to judge the next bit until The number of digits is less than r, then It is the CRC8 checksum.

3. The information compilation technology method based on Julia fractal set according to claim 1, characterized in that: The step S1 of mapping it into a complex number to generate a Julia set image with specific fractal features is further as follows: mapping the binary ASCII code into a real number, as the real part a in the complex number c=a+bi, and the imaginary part b is fixed to -0.2, to generate a Julia set with specific fractal features. The image is iteratively calculated according to the value of the complex number c to generate the Julia set image, and the binary image is generated through threshold processing.

4. The information compilation method based on Julia fractal set according to claim 3 is characterized in that: The Julia set The image is further: 1) For a complex function ,in is a complex number, x and y are real numbers, , is also a complex number, a and b are real numbers; 2) From an initial plural To begin, for the function Iterate and get a sequence ,in ; 3) For a given c, define the Julia set For all such that the iterative sequence Bounded initial value gather.

5. The information compilation technology method based on Julia fractal set according to claim 1, characterized in that: The step S2 is further to 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 containing the fractal set, which is a rectangular region; 2) Choose a range of different values, usually starting with a larger value and gradually decreasing; 3) For each value, use small squares or cubes with a side length of to cover the fractal set, and count the number of small squares or cubes required; 4) Plot a graph with as the ordinate and as the abscissa, and use linear regression method to find the slope of the straight line. The slope is the approximate value of the box dimension, that is, the fractal dimension D1.

6. The information compilation technology method based on Julia fractal set according to claim 1, characterized in that: The step S3 further includes: saving the generated binary image in PNG format, and storing 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; and using the Pandas library to read and process Excel files to facilitate the management of the database.

7. The information compilation technology method based on Julia fractal set according to claim 1 is characterized in that: In the decoding process of step S4, the fractal dimension D2 of the fractal image is obtained, and the original information is reversely deduced based on this as an index, and further comprises: reading the fractal image to be decoded and extracting its metadata; converting the image into a binary image, and obtaining its fractal dimension D2; in the `read_database` function, reading data from the database and building an index, and finding 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, reversely indexing the real part of the complex number c in the database, and then reversely deriving the ASCII code, and finally restoring the original input character; When the imaginary part b in the complex number c=a+bi is fixed to 0, that is, c=a is a real number, a piecewise cubic polynomial function can be constructed using cubic spline interpolation ,make In each subinterval [ ] is a cubic polynomial and satisfies: 1) , i=0,1…n, that is, the value of the spline function at a given data point is the same as the original data; 2) In the whole range has continuous first-order and second-order derivatives; In this way, the direct mapping of the fractal dimension D2 to the real part of the C value can be directly realized. However, when the imaginary part of the C value is not 0, the data heterogeneity is too strong, and the data mapping is realized by dynamic database retrieval matching.

8. The information compilation technology method based on Julia fractal set according to claim 1, characterized in that: The step S4 of using fractal self-similarity to realize error correction further comprises: using ridge regression, setting a regularization parameter, that is, an alpha value of 0.001, obtaining a local and overall relationship between the fractal code symbol carrier, calculating the fractal dimension value of the undamaged local area of ​​the fractal code by a box counting method, and obtaining a plurality of local fractal dimension values; establishing a mapping relationship between the local fractal dimension value and the overall fractal dimension value through a large amount of experimental data or theoretical analysis; Substitute the extracted local fractal dimension value into the mapping relationship, calculate the overall 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 based on the difference; If the difference is too large, it is determined that the error cannot be corrected.

9. The information compilation method based on Julia fractal set according to claim 7, characterized in that: The parallel search strategy of step S4 is further as follows: an adaptive block dynamic search algorithm is adopted to dynamically adjust the search strategy according to the data range and block size, and the original information is reversely derived through the parallel search algorithm according to the real part of the complex number c, the original string length, the total number of bits and the checksum, and the checksum is verified.

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