Inkscape 0.48 Windows 7
So I've been working on this for about 4 years now. lol
4 years ago I made a tiled clones spiral by grouping a star with a spiral.
But that's not really what the Manual is doing.
The "logarithmic spiral" refers to the Base parameter in the Tiled Clones Menu.
Back in 2007 I moved the center rotation (crosshair) by grouping objects with a rectangle.
I think this may have changed over the years, but anyway, this time I just moved the crosshair on the object.
Select object with the Select/Transform Tool, click again and the arrows change and the crosshair appears. Drag the crosshair.
This is my star I used for the tiled clones spiral.
My spiral is not as perfect as the manual's spiral. But if I use the Base parameter of 2.7 my spiral gets so huge I can't display the entire thing on my screen even at 1% zoom. So, I used a Base of 2.0 and was content. :) From my understanding, the Base has to do with the stars not bumping into each other as they spiral around. Even at Base 2.7 my stars still bumped into each other in the center.
Other than the Base difference, I think my parameters are the same. My spiral looks different than the manual's spiral, but I'm happy with what I accomplished.
Zoom of center:
(Setup in Inkscape, edited in Paint Shop Pro.)
The other spiral challenges: