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     Fraction dimention become a way of  measuring   qualities    that
otherwise have no  clear  definition:  the  degree  of  roughness   or
brokeness or irregulary in an object. The objects that have   fraction
dimension  are  called  fractals.                                     
                          The Koch snowflake.                         
     To  construct Koch snowflake, begin with a triangle with sides of
length 1. At  the middle of each side, add a new triange one-third the
size;and so  on. The length of the boundary is  3*4/3*...-infinity.Yet
the   area   re- mains less than  the   area   of   a   circle   drawn
around the original triangle.  Thus an infinitely long line surrounded
a finite  area.The outline of the Koch curve does fill the space.   It
is  more  than  a line,yet  less  than  a  plane.  It is greater  than
one-dimensional, yet less than  a two-dimentional    form.   For   the
koch  curve,  the ingfinitely extended multiplication  by  four-thirds
gives  a dimention of 1.2618.                                         
