递回关系-雪花曲线.ppt

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1、遞迴關係－雪花曲線次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n4n×(1/3)nvonKochCurve第0迴次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n4n×(1/3)nv

2、onKochCurve第1迴次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n4n×(1/3)nvonKochCurve第2迴次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n4n×(1

3、/3)nvonKochCurve第3迴次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n4n×(1/3)nvonKochCurve第4迴次數段數每段長度全長011114(1/3)41×(1/3)1242(1/3)242×(1/3)2343(1/3)343×(1/3)3444(1/3)444×(1/3)4545(1/3)545×(1/3)5…n4n(1/3)n

4、4n×(1/3)nvonKochCurve第5迴SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/9)∆3×40×(1/9)1∆23×423×4(1/9)2∆3×41×(1/9)2∆33×433×42(1/9)3∆3×42×(1/9)3∆43×443×43(1/9)4∆3×43×(1/9)4∆53×453×44(1/9)5∆3×44×(1/9)5∆…n3×4n3×4n-1(1/9)n∆3×4(n-1)∆×(1/9)n∆第0迴SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/

5、9)∆3×40×(1/9)1∆23×423×4(1/9)2∆3×41×(1/9)2∆33×433×42(1/9)3∆3×42×(1/9)3∆43×443×43(1/9)4∆3×43×(1/9)4∆53×453×44(1/9)5∆3×44×(1/9)5∆…n3×4n3×4n-1(1/9)n∆3×4(n-1)∆×(1/9)n∆第1迴SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/9)∆3×40×(1/9)1∆23×423×4(1/9)2∆3×41×(1/9)2∆33×433×42(1/9)3∆3×42×

6、(1/9)3∆43×443×43(1/9)4∆3×43×(1/9)4∆53×453×44(1/9)5∆3×44×(1/9)5∆…n3×4n3×4n-1(1/9)n∆3×4(n-1)∆×(1/9)n∆第2迴SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/9)∆3×40×(1/9)1∆23×423×4(1/9)2∆3×41×(1/9)2∆33×433×42(1/9)3∆3×42×(1/9)3∆43×443×43(1/9)4∆3×43×(1/9)4∆53×453×44(1/9)5∆3×44×(1/9)5∆

7、…n3×4n3×4n-1(1/9)n∆3×4(n-1)∆×(1/9)n∆第3迴SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/9)∆3×40×(1/9)1∆23×423×4(1/9)2∆3×41×(1/9)2∆33×433×42(1/9)3∆3×42×(1/9)3∆43×443×43(1/9)4∆3×43×(1/9)4∆53×453×44(1/9)5∆3×44×(1/9)5∆…n3×4n3×4n-1(1/9)n∆3×4(n-1)∆×(1/9)n∆第4迴SnowFlake第4迴SnowFlake第4迴

8、SnowFlake次數段數增加面數每面面積增加面積0311∆∆13×43(1/9)∆(1/9)1∆×3×40∆23×423×4(1/9)2∆(1/9)2∆×3×41∆33×433×42(1/9)3∆(1/9)3∆×3×42∆43×443×43(1/9)4∆(1/