???? ?????? fractal dimension calculation using the

1
???? ?????? fractal dimension calculation using
the counting box method

• ??????
• PP23
• ???? ????
• ??? ??????

2
???? ???????

• ??? ????? ?
• ??? ???? ?????? ?
• box counting - ????? ???? ??????
• ?? ????? .
• ?????? ???????.
• ?????? ??????.

3
??? ??????

• ????? ?????????? ??????? ?????? ?"? ???? ??
  ??????? ??????.

4
??????? ?????? ??????

1. ?? ??? ??.
2. ??????.
3. DNA???? ??.

5
??? ???? ???????

• ??? ???? ???.
• ??? ??? ??????
• ?????? ????? ??????.

6
????? ???????

• ??? ????? ?? ??? ??????
• ?????? ??????? ??? ??? ????? ???? ???? ?? ??? ??
  ?????, ????? ???? ??????.
• (FRACTAL ???)

7
????? ????? ???????

• ?????? ????? ??????? ?? ????? ????? ????? "box
  counting".

8
Box counting

• ???????? ?????? ???? ?????? ?? ??? ????? ??? ???
  ???? ???????? ????? ???? ???????? ????? ??????.
• Dlim Log (N) / Log (1/L)
• - N ???? ??????? , L - ???? ?????
• - D ???? ??????
• ??? ????? ?????? ????? ????? ?? ?????

9
?????

• ???? ????? ?????? ??????.

10
?????

• ????? ????? ????? ???????.(0 ? 1)

11
?????

• ????? ???.

12
?????

• Box size 12 x 12 pixels

13
?????

• Box size 6 x 6 pixels

14
?????

• Box size 3 x 3 pixels

15
??????
16
??????

• ????? ???????? ??????

17
Box counting

• ?????? ?????? ??? ????? ??????? ?? ??????.

18
Box counting

• ???????? ?????? ???? ?????? ?? ??? ????? ??? ???
  ???? ???????? ????? ???? ???????? ????? ??????.
• Dlim Log (N) / Log (1/L)
• - N ???? ??????? , L - ???? ?????
• - D ???? ??????
• ??? ????? ?????? ????? ????? ?? ?????

19
?????? ??????

• pvm-embaraslly parallel

20
?????? ??????

• Load balancing

21
?????? ?????? - ??????

• ????? ?????? 1. ???? ??????.
• 2. ?????? ??????.
• 3. ??????.
• ????? ???? ?????? ???????? ?? ???? ?????? .

22
??????

• http//www.ees.nmt.edu/davew/P362/boxcnt.htm
• www.snunit.k12.il

23
????