To calculate the dimension of grap of function, the minimum boxes can be replaced by the variation of fractal interpolation function, and the box-dimension formula can be proved from another angle.Based on the study of the properties of variation of bivariate continuous function,the variation of recurrent fractal interpolation function is estimated on the rectangular domain,which provides a new method to study dimension of recurrent fractal graph.
ZHANG Wenjing
,
FENG Zhigang
. Variation of recurrent fractal interpolation surface[J]. Journal of Hebei University(Natural Science Edition), 2016
, 36(4)
: 349
-352
.
DOI: 10.3969/j.issn.1000-1565.2016.04.003
[1] BARNSLEY M F.Fractal everywhere[M].New York:Academic Press,1988.
[2] BARNSLEY M F,ELTON J H,HARDIN D P.Recurrent iterated function systems[J].Constr Approx,1989,5:3-31.
[3] 沙震,阮火军.Bamsley-Elton Hantin的一个定理的修正[J].高校应用数学学报A辑,2000,15(2):157-162. SHA Z,RUAN H J.A revision of the theorem of the Bamsley-Elton Hantin[J].Appl Math J Chinese Univ Ser A,2000,15(2):157-162.
[4] TRICOT C.Curves and fractal dimension[M].New York:Spinger,1995.
[5] DUBUC B,TRICOT C.Variation dune Function et Dimension de son graph[J].C R Math Acad Sci ParisSer I,1998,306:531-533.
[6] TRICOT C.Funtion norms and fractal dimension[J].Siam J Math Anal,1997,28(1):189-212.
[7] DUBUC B,ZUKER S W,TRICOT C,et al.Evaluating the fractal dimension of surfaces[J].Proc R Soc Lond Ser A,1989,425:113-127.
[8] 文志英.分形几何的数学基础[M].上海:科学出版社,2000. WEN Z Y.The mathematical basis of fractal geometry[M].Shanghai:Science Press,2000.
[9] 冯志刚,王磊.分形差值函数的变差的性质[J].江苏大学学报(自然科学版),2005,26(1):49-52. FENG Z G,WANG L.Properties of variation of fractal interpolation function[J].Journal of Jiangsu University(Natural Science),2005,26(1):49-52.
[10] FENG Z G.Variation and Minkowski dimension of fractal interpolation surface[J].Math Anal Appl,2008,345(1):3222-344.
[11] 徐惠,冯志刚.一类分形插值函数的变差和计盒维数[J].安徽工业大学学报(自然科学版),2008,25(4):444-447. XU H,FENG Z G.A class of variation and box-counting dimension of fractal interpolation function[J].Journal of Anhui University of Technology(Natural Science),2008,25(4):444-447.
[12] 王伟,冯志刚.递归分形插值函数的计盒维数[J].安徽工业大学学报(自然科学版),2009,26(2):187-189. WANG W,FENG Z G.Box-counting dimension of recurrent fractal interpolation function[J].Journal of Anhui University of Technology(Natural Science),2009,26(2):187-189.
[13] BOUBOULIS P,DALLA L.A general construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension[J].Japprox Theory,2006,141:99-117.
