function?frac_dim?=?boxcount（coordmat?maxstep?plotflag）

%?frac_dim?=?boxcount（coordmat?maxstep?plotflag）
%?calculates?the?fractal?dimension?of?a?set?in?the?2D?plane?
%?using?the?box?counting?method.
%
%?INPUT:??coordmat????coordinates?of?the?set?points
%?????????maxstep?????maximum?step?number?for?the?boxcounting?method
%?????????plotflag????=?0?do?not?plot?anything
%?????????????????????=?1?plot?some?stuff
%
%?OUTPUT:?frac_dim????the?estimated?fractal?dimension

%?AUTHOR:?Bernd?Flemisch?IANS?University?of?Stuttgart
%?VERSION:?1.0?21.10.2004
%?EMAIL:?flemisch@ians.uni-stuttgart.de

if?nargin?	error（[‘At?least?two?input?arguments?are?required.?Please?type?‘?...
	???????‘‘‘help?boxcount‘‘?for?usage?information.‘]）;
end
if?nargin???plotflag?=?0;
end

glob_llx?=?min（coordmat（:1））;?%?lower?left?corner?of?the?initial?box?x-coordinate
glob_lly?=?min（coordmat（:2））;?%?lower?left?corner?of?the?initial?box?y-coordinate
glob_urx?=?max（coordmat（:1））;?%?upper?right?corner?of?the?initial?box?x-coordinate
glob_ury?=?max（coordmat（:2））;?%?upper?right?corner?of?the?initial?box?y-coordinate
glob_width?=?glob_urx?-?glob_llx;?%?width?of?the?initial?box
glob_height?=?glob_ury?-?glob_lly;?%?height?of?the?initial?box
x?=?zeros（maxstep+1?1）;?%?data?for?the?least?squares?method
y?=?zeros（maxstep+1?1）;?%?data?for?the?least?squares?method

for?step?=?0:maxstep?%?loop?over?the?subdivision?steps?
??n_boxes?=?0;?%?number?of?boxes?containing?points?of?the?set
??n_sds?=?2^step;?%?number?of?subdivisions?in?one?direction?
??loc_width?=?glob_width/n_sds;?%?width?of?one?box
??loc_height?=?glob_height/n_sds;?%?height?of?one?box
??for?sd_x?=?1:n_sds?%?loop?over?local?boxes?in?x-direction
????loc_llx?=?glob_llx?+?（sd_x?-?1）*loc_width;?%?lower?left?corner?x-coordinate
????loc_urx?=?glob_llx?+?sd_x*loc_width;?%?upper?right?corner?x-coordinate
????%?detect?the?set?points?inside?the?strip?[loc_llx?loc_urx]:
????found_idx?=?find（（coordmat（:1）?>=?loc_llx）?&?（coordmat（:1）?????found_y?=?coordmat（found_idx?2）;?%?the?y-coordinates
????for?sd_y?=?1:n_sds?%?loop?over?local?boxes?in?y-direction
??????loc_lly?=?glob_lly?+?（sd_y?-?1）*loc_height;?%?lower?left?corner?y-coordinate
??????loc_ury?=?glob_lly?+?sd_y*loc_height;?%?upper?right?corner?y-coordinate
??????%?detect?the?set?points?inside?the?local?box:
??????inside_idx?=?find（（found_y?>=?loc_lly）?&?（found_y???????if?（length（inside_idx）?>?0）
	n_boxes?=?n_boxes?+?1;?%?local?box?contains?points?of?the?set
??????end
????end?%?loop?over?local?boxes?in?y-direction
??end?%?loop?over?local?boxes?in?x-direction
??x（step+1）?=?step*log（2）;
??y（step+1）?=?log（n_boxes）;
end?%?loop?over?the?subdivision?steps?

%?To?estimate?the?fractal?dimension?the?slope?of?the?line?
%?“closest“?（in?the?least?square?sense）?to?the?points?（xy）?is?calculated:
A?=?zeros（maxstep+1?2）;?%?set?up?the?matrix
A（:?1）?=?x;?%?the?first?column
A（:?2）?=?ones（maxstep+11）;?%?the?second?column?
[QR]?=?qr（A）;?%?comput

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3421??2004-12-08?10:25??boxcount.m

?????文件????????291??2004-12-08?10:25??fd_sierp.m

?????文件???????1165??2004-12-01?16:55??sierpinski.m

-----------?---------??----------?-----??----

?????????????????4877????????????????????3