Fractal Characteristics and Fractal Dimension Measurement on

Fractal 的论文。

!"#$%&’"$()"*+,-#"./*0-,1,234+5267".8490,"#":7;<-64+$=92$>?$<-+$%&&@

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"#$%#&’(#"#$%)"*+%*$+#,-!"#$%#&.*/),+*0,1)#+2")/),%0,

3"04),52"6#$)+067&2/*,2/8&)$%"*$90"$)&#*,"

!"#$%&’()*+

%,-."++’+/

（.):%;061#%)"*#&5$*),$)#,-<)$(,0&0=>，?*’#,@,*A)"+*%>065$*),$)#,-<)$(,0&0=>，?*’#,A(&&@B，’(*,#）

7B+%"#$%：!"#$"%&%$’#&()’($)*+,&*-#.)/&+%$#)0#&#&#)#%&$"#1,2%)$%..(.3#4#$’&*.5($&*)$*6#（789）%.1%&#+4#$’(*.5($&*)$*6#，%.1’"#+&%$’%41(5#.)(*.)*+,&*-#.)/&+%$#)0#&#5#%)/&#1,2’"#74(’:)4%.15#’"*1;!"##<6#&(5#.’%4&#)/4’)(.1($%’#’"%’’"#,&*-#.)/&+%$#*+%4/5(./5#4#$’&($6*&$#4%(.()%+&%$’%4,*12(.)’%’()’($)，%.1’"#+&%$’%41(5#.)(*.)*+,&*-#.)/&+%$#)%&#1(++#&#.’0(’"’"#1(++#&#.’%564(+($%’(*.5/4’(64#=%4>

,*’"*+=%4/#)5#%)/&#1(.(&&C/.1#&&#+4#$’(*.5($&*)$*6#%.1(./#;:.%44*+5#%)/&#1+&%$’%41(5#.)(*.)，

@&&C/.1#&789%&#5%<(5/5，0"#&#%)’"#=%4/#)5#%)/&#1(.DEC/.1#&&#+4#$’(*.5($&*)$*6#%.1(.%&&&C/.1#&789%&#*,=(*/)425(.(5/5;!"#+&%$’%41(5#.)(*.)*+,&*-#.)/&+%$#)%&#%4)*%++#$’#1,2’"#1#3&##)*+3&%2$*56%&()*.%.1’"#-(.1)*+5#%)/&(.35#’"*1);!"#&#4%’(*.)"(6),#’0##.’"#+&%$’%41(5#.)(*.)*+,&*>-#.)/&+%$#)%.16*&$#4%(.,#.1)’&#.3’")%&#’"%’’"#2%&#(.6*)(’(=#$*&&#4%’(*.*.’"#4*05/4’(64#)%.1(..#3%>’(=#$*&&#4%’(*.*.’"#"(3"5/4’(64#);

C)>D0"-+：,&*-#.)/&+%$#；+&%$’%41(5#.)(*.；74(’:)4%.15#’"*1；#4#$’&($6*&$#4%(.

(E,%"0-2$%*0,

G#*N2,*N4#496+29H"+94#-2,50-34R44,T2?4#7*54?-55*HH"+62,:9"NH",4,652,4#496+29267M6+-,5N2552",2,M?*56+7$<4-,T02#4，604-#*N2,*N4#496+29H"+94#-2,5-+4-U2,?".N-64+2-#5T260N-,7H0-545，T02902,9#*?49+75M6-##2,4，:#-55-,?:-5$L+"."*,?+454-+9045",R+"U4,5*+M.-945".-#*N2,*N4#496+29H"+94#-2,-+4R4,4.292-#6"2,?2M9-62,:604N490-,29-#90-+-964+256295".60454H"+94#-2,5$

［(］

2,(WAE."+N-##7R+"*:06*H604=2,94<-,?4#R+"6VV

604.+-96-#604"+70-5+-H2?#7R44,?4M9",94H6"..+-96-#，

34#"H4?-,?R49-N4-,4T#7-+254,N-604N-6295R+-,90，-,?-902434?6044S64,5234-HH#29-62",2,N-,7.24#?5$X6R49-N4",4".604N"56H"T4+.*#6""#52,Y*-,626-6234#756*?72,:-,??459+2R2,:9"NH#29-97".50-H4，9",56+*962",

604.+-96-#-,?.*,962",2,,-6*+4$X,+494,66T"?49-?45，

604"+70-?:"6N-,7-?3-,945",R+"U4,5*+.-945".N46-#-,?+"9UN-64+2-#5$X,60"54+454-+9045，N-,7N460"?50-?R44,546*H6"N4-5*+4.+-96-#?2N4,52",5，Y*-,626-M6234#7?459+2R4604?4:+44".+"*:0,455-,?-,-#7O4604+4M#-62",502H5R46T44,604.+-96-#?2N4,52",-,?604H-+-N4M

［%MW］

$G##".60"54H+"32?4?-64+5".N-64+2-#N490-,295

,4TT-7."++454-+9045",R+"U4,5*+.-945$8025H-H4+-2N4?6"?259"34+604.+-96-#H+"H4+6245，.+-96-#?2N4,52",5-,?+4#-62",5R46T44,.+-96-#?2N4,52",-,?N-64+2-#N4M90-,295",R+"U4,5*+.-945".604-#*N2,*N4#496+29H"+94#-2,R7*52,:604.+-96-#604"+7$

X,"R54+3-62",".604?46-2#5",R+"U4,5*+.-945，26

（F494234?：)-,$(A，%&&B；G994H64?：=4H$(B，%&&B）

（杨志远）：IG’JK027*-,G55"9$L+".$；>MN-2#：7O7BBBP(DE$

9"N

T-5?259"34+4?60-6604+"*645".9+-9U54SH-,?2,:2,N-M64+2-#*5*-##7#""U#2U4K2:MK-:，4-90",4564HT-52++4:*M#-+T260+"*645".?2..4+4,652O4-,??2..4+4,6?2+4962",，H-+629*#-+#72,60459"H4".9+-9U5H+4552,:-R2:?#4664+$804+4T4+4-:-2,5N-##9+-9U5H+4552,:?#4664+2,?2..4+M4,6,4562,:N29+"56+*96*+45$804+4."+4R+"U4,5*+.-945T4+460"*:06-554#.M9"NH-+-R2#267-,?.+-96-#56+*96*+452,-94+6-2,59"H45$<-,?4#R+"6VVN-?4604.2+56.+-96-#

［%］

+454-+9045",R+"U4,5*+.-9452,(WZB$[40-5.2,2504?604Y*-,626-6234-,-#7525".6042++4:*#-+267",N46-#R+"MU4,5*+.-945R7*52,:604.+-96-#N460"?-,?H+4?2964?6049-H-R2#267"..+-96-#?2N4,52",-5-:4"N46+29H-+-N464+2,?459+2R2,:60490-+-964+256295".R+"U4,5*+.-945$\02,454

［E，［W］B］

，<*K-2Y2,，^24590"#-+5，5*90-5]*,:\02T42

［@］

#’%4，56*?24??44H#7",N46-#-,?+"9UR+"U4,5*+M[

.-945."+-#",:H4+2"?，-,?60"*:0660-6604N-64+2-#R+"MU4,5*+.-9450-?.+-96-#90-+-964+256295$<4-,T02#4，6047."*,?60-6.+-96-#5",R+"U4,5*+.-9450-346T"H+"H4+6245：.2+56#7，54#.M9"NH-+-R2#267_*564S25652,56-6256295，5".+-9M6-#H04,"N4,-_*56-+42,56-6256295$=49",?#7，.+-96-#5",N-64+2-#R+"U4,5*+.-945-+4N*#62M59"H4.+-96-#5，-,?604+44S256?2..4+4,6.+-96-#56+*96*+452,?2..4+4,659"H45$>#496+29H"+94#-2,N-64+2-#5-+452N2#-+6"604+"9U",452,60456+*96*+45$80*5，6042+.+-96-#90-+-964+256295",R+"MU4,5*+.-9454S25652N2#-+#72,56-6256295$

%

%;(

8F:)"*/),%#&

1#%)"*#&+#,-:")%")#%/),%

8045-NH#452,4SH4+2N4,65T4+490"54,.+"NN2?M?#4M2,64,52",R-+5，T0290T4+4!%&NNC%&&NN2,52O4-,?52,64+4?-6(%Z&‘2,-N-,*.-96*+46*,,4#U2#,".-,

Fractal 的论文。

.@

!"#$%&