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Title:

IFS??

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Title: 1 --- Author: Chen Falai Last modified by: office Created Date: 5/18/1999 12:27:32 PM Document presentation format – PowerPoint PPT presentation

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Tags: ifs | sierpinski

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Title: IFS??


1
?????????(2)---??
  • ???????????
  • ???

2
????
  • ??????
  • ????
  • ????
  • IFS??
  • ?????

3
1??????
  • ??????
  • ????????????????
  • ???,????---??
  • ?? 1,Cantor??

4
Cantor ?? ??????(??????!),????????! ??
2,Weierstrass?? ?? 1ltslt2 ? ,W(x)
?????? ??????????? s1.4, ????
5
?? 3,Van Koch ????
6
???????? ????????????????? ?????????,?????????
???????????????? B. Mandelbrot ?????????Van
Koch ?????,????????? ?????????---??(Fractal)
??????????
7
  • B. B. Mandelbrot

8
  • ?????
  • 1??????????
  • 2??????????
  • 3????????,????????
  • ????
  • 4??????
  • 5????????,???????
  • ???????,????????

9
  • ?????
  • 1???????? F ?????,? F ? m ?????,?????? c ???
    F??,??? F ????
  • ??,??Cantor?,
  • ??Van Koch ????,

10
  • ???????,????,????????1/N,???N??
  • ???????????N?,??N2??????
  • ???????????N?,??N3??????
  • ???,????????m?????????,?????????1/c.
    ??????D??cDm.

11
2?????? ?????,?? R ?????? R ?????
??????? ???????? F ????????????? F
?????? ??,?? Weierstrass?????????????,?????
? s.
12
  • ???????
  • 1???????
  • 2???????,????????
  • 3???????,
  • 4????????
  • 5???????
  • 6?????????
  • ?????,??,??,????

13
2?????????
  • ?????? ,??????
  • ???????
  • ??????
  • ????????,???? ??????

14
??,Cantor ?????? Van Koch ?????????
????
15
2?Minkowski ??
16
3?Sierpinski??
17
4????
18
5?Hilbert??
19
6?????(L??)
  • ????Lindenmayer?????L????????????????
  • ??V?????????,
  • w?????,
  • P?????

20
  • ??,F??????d, ?????a,
  • -?????,????,?????

21
6?????(L ??)
22
(No Transcript)
23
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24
3??????????
  • ?Z????,??????????
  • f(Z)???????
  • ????????? ,??????
  • ????????? ,????
  • ??????

25
  • Julia?
  • ????????
  • ????? c,?????? ????? ????????????Julia?,??
  • ???? ??

26
  • Mandelbrot?
  • ???? ,??????(2)????? c ????????????
    Mandelbrot???
  • ???? ??
  • ?
  • ?(2)??

27
  • Julia ??????
  • 1????? p,q, ??????? N, ????? a,b, ??????? K.
  • 2????????
  • 3???? ??
    ???,??????????? ??(3)??????????
    ?? ,????(i, j) ??????????? n ??,
    ,???? (i,j)???? n mod K?

28
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29
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30
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31
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32
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33
4?IFS??????
  • ????
  • ???????A, B, C????????? , ?????

?????????
?????????
?????????
??????????,??????????????????
34
(No Transcript)
35
  • IFS??
  • IFS--Iterated Function System
  • ?? n ?????
  • ?? n ???
  • ???? ,??? ????
  • ????
  • ??? ?????????IFS????

36
  • ?IFS???????
  • 1?????????
  • ????L ????????,??????N?
  • 2?? V ?? ???,??? ? ????????
    ???N?????? ??????? ??? (i,j)????

37
  • ????
  • Cantor ?

38
???
39
(No Transcript)
40
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41
  • ??IFS??????????????????????,?? IFS ????,?????????
    ,????????
    ,?
  • ???IFS??????????????? IFS ???????

42
5?????
43
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44
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45
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46
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47
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48
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49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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61
????
62
(No Transcript)
63
????
  • ????
  • www.geocities.com/SiliconValley/Haven/4386
  • http//www.fractal.com.cn/fxiy/index.htm

64
????
  • http//www.fractal.com.cn/fxyy/fs/fs005.htm
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