Calculation Of Hausdorff Measure For A Class Of Self-Similar Set

Fractal geometry is a new discipline developed in the 1970s,The main research object are irregular geometric figures,Such as grotesque clouds,molecular movement of the track without rules,Meandering coastline and more.And its ideas and methods have infiltrated into various disciplines,even if the fractal geometry has a wide range of applications.However,its own theory research is not particularly easy.especially for the computation of the fractal set Hausdorff dimension and measure,In spite of the self-similar set,the calculation of the Hausdorff measure is also particularly difficult.This paper mainly discusses the calculation of the Hausdorff measure of a class of self-similar set S in a plane and a self-similar set W in three-dimensional space.The full text is divided into four chapters.The first chapter discusses the back-ground of this article and the current status of fractal geometry.The second chapter gives a detailed description of the basic definitions of fractal sets and related lem-mas.In the third chapter,a class of self-similar sets S is first constructed in the plane,then the upper and lower bounds of S are estimated,Get the exact value of S's Haus-dorff measure,which is H1(S)?(?),Also got a corollary,when the similarity ratio is 1/r(0<1/r<1/5)and s = logr3 + log3/5/log1/r,we get HS(S)=((?))s,where s is the Hausdorff di-mension.In chapter IV,Considering a class of self-similar sets W generated in the unit cube,by using the principle of natural covering and the principle of mass distribution,the upper bound is(?)and the lower bound is(?).Thereby H1(W)=(?).