CAJ | 학술논문

分析傅里叶级数迭代映射的特点，以矩阵乘积的运算形式为工具，构造截断傅里叶级数对应的平面动力系统。运用蒙特卡罗搜索法选定参数向量，并通过李雅普诺夫指数确定动力系统的动力学特性，构造出周期窗口内的混沌吸引子。任意周期窗口间相应点之间的对应关系是线性的，因此构造出的图案是连续的且结构相同的。选用任意的周期窗口作为基本计算区域，提出构造出平面排列图案的算法。实验结果表明，采用文中算法可以生成大量的平面等距排列的混沌吸引子图案。
분석부리협급수질대영사적특점，이구진승적적운산형식위공구，구조절단부리협급수대응적평면동력계통。운용몽특잡라수색법선정삼수향량，병통과리아보낙부지수학정동력계통적동역학특성，구조출주기창구내적혼돈흡인자。임의주기창구간상응점지간적대응관계시선성적，인차구조출적도안시련속적차결구상동적。선용임의적주기창구작위기본계산구역，제출구조출평면배렬도안적산법。실험결과표명，채용문중산법가이생성대량적평면등거배렬적혼돈흡인자도안。
To analyze the characteristics of the iteration mapping with truncated Fourier series, this paper used the operation of matrix product as tool and constructed the planar dynamic systems with truncated Fourier series. Monte Carlo method was used to search the parameter vectors in the parameter space. The Lyapunov exponent was used to judge the characteristics of dynamical systems. We construct Chaotic attractors in the cyclic windows. It is linear, then clarifying the relationship of corresponding points between any cyclic windows. The respective images are continuous and same structures. We can choose any cyclic windows as the basic computing region, which is transferred to the plane to compose the planar tilling. Experimental results show the effectiveness of the proposed approach.