《计算机应用研究》|Application Research of Computers

基于马尔可夫链的分形图形生成算法

Fractal image generation algorithm based on Markov chain

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作者 邓贞宙,赵欣,王平,洪伟毅,陶凌,余礼苏
机构 1.南昌大学 信息工程学院,南昌 330031;2.华南师范大学 信息光电子科技学院,广州 510006
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文章编号 1001-3695(2021)10-055-3189-07
DOI 10.19734/j.issn.1001-3695.2020.12.0565
摘要 区别于传统的基于欧几里德算法的图形生成算法,在迭代函数系统的基础上,提出了一种基于马尔可夫链的分形图形生成算法。该算法首先利用马尔可夫链为每个状态转移函数设置转移的概率密度,其次通过比较随机数与状态转移函数的概率分布来确定进入的状态转移函数,进而计算吸引点的位置、确定线条的位置和角度,推导出迭代后线条的角度关系,最后通过多次迭代生成不同角度和位置的线条组成一个完整的图形。相对于传统算法,该算法针对分形图形的生成、仿射变换矩阵参数的具体调控方式以及图形散点图的变化规则进行研究,通过对不同分形图形的生成及其形态调控的仿真实验验证了该算法可以对分形图形生成过程进行描述,进一步验证了该算法的优越性。
关键词 欧几里德算法; 迭代函数系统; 马尔可夫链; 分形图形生成算法; 状态转移函数
基金项目 国家科技部03专项(20193ABC03A040)
国家自然科学基金青年项目(61501197)
江西省创新创业高层次人才“千人计划”创新人才长期项目(S2018LQCQ0554)
澳门青年学者计划资助项目(AM201921)
广东省微纳光子功能材料与器件重点实验室(91180198)
2019年江西省研究生创新专项资金立项项目(YC2019-S109)
广东省科学技术厅(2020B1212060067)
计算机体系结构国家重点实验室开放课题(CARCHB202019)
国家自然科学基金地区项目(62161024)
中国博士后科学基金特别资助(站前)项目(2021TQ0136)
本文URL http://www.arocmag.com/article/01-2021-10-055.html
英文标题 Fractal image generation algorithm based on Markov chain
作者英文名 Deng Zhenzhou, Zhao Xin, Wang Ping, Hong Weiyi, Tao Ling, Yu Lisu
机构英文名 1.School of Information Engineering,Nanchang University,Nanchang 330031,China;2.School of Information & Optoelectronic Science & Engineering,South China Normal University,Guangzhou 510006,China
英文摘要 Different from the traditional graph generation algorithm based on the Euclidean algorithm, on the basis of the iterative function system, this paper proposed a fractal graph generation algorithm based on the Markov chain. Firstly, this algorithm used the Markov chain to set the transition probability density for each state transition function. Secondly, this algorithm compared a random number with the probability distribution of the state transition function to determine the entered state transition function, then it calculated the position of the attractive point and determined the position and angle of the line, thus derived the angle relationship of the line after iterations. Finally, the lines of different angles and positions generated a complete graph after several iterations. Compared with the traditional algorithm, this algorithm focused on the generation of fractal graphs, the specific control method of the affine transformation matrix parameters, and the changing rules of the graph scatter graph. By setting simulation experiments, it verifies that the proposed algorithm can not only generate different fractal graphs but also regulate its shape. In addition, the proposed algorithm can describe the generation process of fractal graphics, which further verifies its superiority.
英文关键词 Euclidean algorithm; iterative function system; Markov chain; fractal graph generation algorithm; state transition function
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收稿日期 2020/12/16
修回日期 2021/2/8
页码 3189-3195
中图分类号 TP391
文献标志码 A