As of v0.46, one can do this with a bit of effort with the logarithmic spiral option of the Create Tiled Clones dialog. This drawing, however, was done by importing the following PostScript program.

%!PS-Adobe-2.0
%% BoundingBox: 0 0 600 600
%% Copyright 2007 Tavmjong Bah
%% Spirals...

/cell {

  gsave
    /y exch def
    /x exch def
    
    x y translate
    x y atan neg rotate
    /mag x x mul y y mul add sqrt 40 div def
    mag mag scale
    newpath
     8.5  0   moveto %
    27    3   lineto
    24.5 27.5 lineto
     0   18   lineto %
    closepath
    stroke

    0.5 setgray
    newpath
      9    1 moveto %
     15    2 lineto
     14    9 lineto
      6.5  6 lineto %
    closepath
    fill

  grestore
} def

% Move to center
300 300 translate

/mmax  13 def % x repeat
/nmax  30 def % y repeat

/theta  8 13 atan def
/sintheta theta sin def
/costheta theta cos def
/2pi 3.141592654 2 mul def
/e 2.718281828 def
/radtodeg 360 2pi div def

/delx 2pi  8 div sintheta mul def
/dely 2pi 13 div costheta mul def 

/myscale 10 def

/n 0 def
nmax {

    /n n 1 add def

    /m 0 def
    mmax {
	
	/m m 1 add def

	/x n delx mul def
	/y m dely mul def

	/xp x costheta mul y sintheta mul sub def
	/yp x sintheta mul y costheta mul add def

	/radical  e xp exp def
	/ydeg yp radtodeg mul def
	
	/xpp radical ydeg cos mul def
	/ypp radical ydeg sin mul def
	
	/xscale xpp myscale mul def
	/yscale ypp myscale mul def

	xscale yscale cell
	
    } repeat
    
} repeat

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