第六单元 分形 作业及参考资料.docx

第六单元分形作业及参考资料

选择：下列哪些系统不是分形？

A.叶脉B.树冠

C.海岸线D.人体

答案：D

选择：谁发明了分形理论？

A.HelgevonKochB.BenoitMandelbrot

C.WaclawSierpinskiD.GeorgCantor

E.AlGore

答案：B

实践：利用UltraFractal软件画自己的分形。

实践：网上找几个规则分型结构，计算一下分形维数。如Koch曲线、谢宾斯基垫、谢宾斯基海绵等。

选择：康托集的分形维数是多少？

A.log2/log3B.log3/log2

C.0.62D.3/4

答案：A

选择：如果在第0级时康托集的长度是10厘米，那么它在第8级时的长度是多少厘米？

A.10×3

C.23×108D.

E.2

答案：E

1.Supposethatlevel0oftheKochcurvestartswithalinesegmentoflength10cm.

Whatisthelengthofthefigureatlevel4(incm)?

A.104

B.10×(4/3)

C.104× (4/3)

D.10× (4/3)4

E.(4/3)10

3.Considerthefractaldefinedinthepicturebelow.Ateachlevel,thesquareisreplaced

byfoursquares,eachofwhichhassideequalto1/3thelengthofthesideatthe

previouslevel.Whatisthefractal(Hausdorff)dimensionofthisfractal?

A.log3/log4

B.log(3/4)

C.log4/log3

D.log(4/3)3

E.log32/log42

4.TheSierpinski“carpet”fractalisdefinedasfollows:

Startwithablacksquare,withsidelengthL.Ateachsucceedinglevel,replaceeach

blacksquarewith8blacksquares,arrayedasshownbelow,eachwithsidelength1/3of

thesidelengthatthepreviouslevel.

Howmanyblacksquaresarethereatlevel10?

A.810

B.80C.128

D.800

E.Noneoftheabove

5.Whatisthefractal(Hausdorff)dimensionoftheSierpinskicarpetfractalfrom

Question4?

A.log4/log3

B.log9/log3

C.log8/log3

D.log64/log8

E.log64/log3

6.WhichofthefollowingvariantsoftheKochcurvehashigherfractal(Hausdorff)

dimensionthantheoriginalKochcurve?

A.AversionwhereeachlinesegmentatlevelTisreplacedbyfourlinesegments,each

1/4thesizeofthelinesegmentatlevelT.

B.AversionwhereeachlinesegmentatlevelTisreplacedbyfourlinesegments,each

1/5thesizeofthelinesegmentatlevelT.

C.Aversionwh