ON COUNTING FUNCTIONS OF SELF-SIMILAR SEQUENCES

被引：0

作者：

KAMETAKA, Y ^{[1
]}

机构：

[1] UNIV TOKUSHIMA,FAC INTEGRATED ARTS & SCI,DEPT MATH & COMP SCI,TOKUSHIMA 770,JAPAN

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1991年 / 38卷 / 1-3期

关键词：

FRACTAL; LEVY CURVE; VONKOCH CURVE; SELF-SIMILAR SEQUENCE; COUNTING FUNCTION; DISCRETE FOURIER TRANSFORM;

D O I：

10.1016/0377-0427(91)90174-I

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A special class of self-similar sequences is considered. They produce fractal self-similar curves such as the Levy curve and the von Koch curve and so on. The counting functions of them are investigated with the aid of the Discrete Fourier Transform. Under suitable conditions on the generator of the self-similar sequence the relative counting function converges to the constant function.

引用

页码：255 / 262

页数：8

共 9 条

[1] Barnsley MF., 2014, FRACTALS EVERYWHERE
[2] RECURRENT SETS
DEKKING, FM
[J]. ADVANCES IN MATHEMATICS, 1982, 44 (01) : 78 - 104
[3] Falconer, 1985, GEOMETRY FRACTAL SET
[4] Feder J., 1988, FRACTALS
[5] Hata M., 1985, JAPAN J APPL MATH, V2, P381, DOI 10.1007/BF03167083
[6] FRACTALS AND SELF SIMILARITY
HUTCHINSON, JE
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) : 713 - 747
[7] Koch H., 1904, ARK MATEMATIK ASTRON, V1, P681
[8] Levy P., 1938, J ECOLE POLYTECH 3, V7-8, P227
[9] Mandelbrot B. B., 1982, FRACTAL GEOMETRY NAT, P1

← 1 →