# Shape-aware archimedean spiral in Illustrator

I'm looking for a way of creating an archimedean spiral from a custom shape in Illustrator, similar to what is discussed in this paper: https://www.microsoft.com/en-us/research/uploads/prod/2020/02/ShapeWordle-InfoVis2019.pdf (under 4.1)

I suspect I would need to write a script for this, which would be way over my level of knowledge. But perhaps there is one already out there?

• I wonder if this could be done by a slanted brush. Mist test in the morning. Jun 8 at 20:33
• As you probably see, keeping the distance of adjacent turns constant doesn't allow the turns to have the same geometric form for every turn except in some lucky special cases; for ex. circle. The forms of the turns suffer less if you allow some distance variation. An example: i.stack.imgur.com/oLHDn.png Jun 9 at 21:59

Ok it is somewhat possible to do this out of the box. There will come a point where it fails since the shapes starts to self intersect (you can expand the results and continue with offsets but ist a bit painful to do). Here is what you do.

You draw a line that is not horisontal but goes down a bit. Then you draw a unpainted box around this that is double the height so that the line start is in center. If you want multiple revolutions you use multiple lines starting at the lowest point of line. Then make this into a art brush and apply to shape.

After that you can move over to offsetting and you get:

after slapping a gradient on the path.

• So you can use a slanted line. Jun 9 at 7:53
• Oh wow, thanks! I will try this out. Jun 9 at 11:46
• I'm not sure if I'm following this correctly, but how do you get it to be one continuous line? For me it looks like this: pasteboard.co/9VjGiQlY1o0r.png Jun 9 at 12:04
• The right end of a line must have exactly the same Y coordinate as the left end of the next line. Otherwise there's no continuity. Jun 9 at 13:11
• @Martin like user said above the lines need to have a spacing that matches the y coordinate of last point on the line on the other side. Remember its the same line its just wrapping around. But now that ive done this a few times i feel its probably better to do one line outward and then offset inward as this hasnt got the same failure conditions even though its a tiny bit more work. Jun 9 at 16:49