Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 130-137.
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Abstract:
In this paper we present a new definition of box dimension, which can be more easily testified compared with the existing definitions. On the basis of this result, we give its simple applications and an algorithm to compute box dimensions of fractal sets.
Key words: Ｆｒａｃｔａｌｓｅｔ, Ｂｏｘｄｉｍｅｎｓｉｏｎ, Ｃｏｖｅｒｉｎｇ, Ｅｑｕｉｖａｌｅｎｔｄｅｆｉｎｉｔｉｏｎ, ＮｕｍｅｒｉｃａｌＣｏｍ ｐｕｔａｉｏｎ
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Wang Wanheng. An equivalent definition of box dimension and its application[J].Acta mathematica scientia,Series A, 1999, 19(2): 130-137.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I2/130
1. ＦａｌｃｏｎｅｒＫＪ．ＦｒａｃｔａｌＧｅｏｍｅｔｒｙ，ＭａｔｈｅｍａｔｉｃａｌＦｏｕｎｄａｔｉｏｎｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：Ｊｏｈｎ Ｗｉｌｌｅｙ ＆ Ｓｏｎｓ，１９９０ ２ ＦｅｄｅｒｅｒＨ．ＧｅｏｍｅｔｒｉｃＭｅａｓｕｒｅＴｈｅｏｒｙ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９６９ ３ ＦａｌｃｏｎｅｒＫＪ．ＴｈｅＧｅｏｅｍｔｒｙｏｆＦｒａｃｔａｌＳｅｔｓ．Ｃａｍｂｒｉｄｇｅ：ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓ，１９８５ ４ 杨海浪．一种求吸引子（ＩＦＳ）分维的有效方法．高等学校计算数学学报，１９９４，１６（３） ５ ＤｕｂｕｃＳ．ＡｐｐｒｏｘｉｍａｔｉｏｎｓｏｆＦｒａｃｔａｌＳｅｔｓ．ＪＣｏｍｐｕｔＡｐｐｌＭａｔｈ，１９９０，２９：７９－８９ ６ 曾文曲，王向阳编著．分形理论与分形的计算机模拟．沈阳：东北大学出版社，１９９３ ７ ＨｅｉｎｚＯｔｔｏＰｅｉｔｇｅｎａｎｄＤｉｅｔｍａｒＳａｕｐｅ．ＴｈｅＳｃｉｅｎｃｅｏｆＦｒａｃｔａｌＩｍａｇｅｓ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８８ ８ 王万恒．迭代函数系统的吸引子的一个逼近算法．贵州大学学报，１９９８，１５（２）；８０－８５
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