CAJ | 학술논문

用三元数方法研究三维分形结构,先定义一种三元数及其运算规则,然后参照Mandelbrot集取集方式定义一种三元数集.用计算机软件以尽可能高的精度对该无穷数集采样取集,按三维点集生成几何外观视图.对整体和重点部位多角度视图的观察分析发现,该数集是一种动物形分形体.三维外观酷似动物,有合乎常理的头、尾、背、腹、鳍和四肢;面部五官具体,一双小眼睛也有眼球、眼窝、眼帘构造;身旁带有与自身相似的子体,子体身旁又带有下一代子体,这种代代相传的相似与几何相似不同,倒与生物遗传相似可比且相仿.数集细微结构多样无尽,局部更高采样密度的点集成像会看到更精细的结构.其复杂形态却是由简单规则生成的,复数分形这一令人费解的特点进而又有三维表现.数集形体存在于欧氏空间原点附近线尺度约为2.3的范围内,其自然特性和细节由文中所附的整体、头部、子体、眼部等多视角图像反映.
용삼원수방법연구삼유분형결구,선정의일충삼원수급기운산규칙,연후삼조Mandelbrot집취집방식정의일충삼원수집.용계산궤연건이진가능고적정도대해무궁수집채양취집,안삼유점집생성궤하외관시도.대정체화중점부위다각도시도적관찰분석발현,해수집시일충동물형분형체.삼유외관혹사동물,유합호상리적두、미、배、복、기화사지;면부오관구체,일쌍소안정야유안구、안와、안렴구조;신방대유여자신상사적자체,자체신방우대유하일대자체,저충대대상전적상사여궤하상사불동,도여생물유전상사가비차상방.수집세미결구다양무진,국부경고채양밀도적점집성상회간도경정세적결구.기복잡형태각시유간단규칙생성적,복수분형저일령인비해적특점진이우유삼유표현.수집형체존재우구씨공간원점부근선척도약위2.3적범위내,기자연특성화세절유문중소부적정체、두부、자체、안부등다시각도상반영.
This paper studies 3D fractal geometry by using the method of the ternary complex number.Based on the definition of the ternary complex numbers and their operation rules,an infinite set of ternary complex numbers is defined according to the rule of Mandelbrot set.Some sample sets are extracted from the set with as high precision as possible,to portray exterior images under the control of the computer software.With observation and analysis,it is shown that its 3D geometric solid is in a shape of an animal.Almost every part of it seems rational,such as the head,tail,back,abdomen and four limbs.Its facial features are idiographic,with eyes equipped by eyeball,eyehole and eyelid.The whole body has some similar subsets around,and each of these subsets itself also has similar subsets around.This similarity differs from the geometrical similarity,but resembles the similarity of biologic heredity.If one increases the density of sample points,more accurate complicated structures can be seen.The zoomorphic fractal solid is located near the origin in Euclid space,its lineal measure is about 2.3.All these natural peculiarities and the details can be seen from the figures.