I would look into developing your complex design as vector in Illustrator:
Create the line with the
Line Segment Tool:
Object -> Expand:
Review the options in the panel:
After ok you should be able to adjust the fill or even apply an outline:
When expanding the lines they will adjust in size if you adjust the artboard in Illustrator.
You could use that to script a variation of sized that were in this article I read once by CSS Tricks titled Favicons, Touch Icons, Tile Icons, etc. Which Do You Need?.
This article led to a generator that could produce everything needed for a webpage named RealFaviconGenerator.
After reading that article I did decide to just create a PNG but since your question asks how to create a favicon I thought I would also provide an Imagemagick solution that can be found here:
convert image.png -bordercolor white -border 0 \
\( -clone 0 -resize 16x16 \) \
\( -clone 0 -resize 32x32 \) \
\( -clone 0 -resize 48x48 \) \
\( -clone 0 -resize 64x64 \) \
-delete 0 -alpha off -colors 256 favicon.ico