[jyl]

Here's what I have so far.

Since all spiders move identically, they remain in a square formation. The square rotates counter clock wise and shrinks in size, always centered at origin. Since each spider's direction of crawl is toward the next vertex of the square (the next spider), the direction of crawl is 45 degrees from the line between spider and origin. So now you can ignore the multiple spiders in a rotating square, just imagine a single spider crawling in a direction 45 degrees from the direction to the origin, which will be a spiral arc. I started to set up the equation for the spider's position, but using cartesian coordinates it got messy and ugly.

I always figure that when a math problem gets messy/ugly, you're most likely doing something the wrong or hard way. I'm told the simple method is to do this using polar coordinates, and the solution is something elegant involving logarithms. I haven't gotten that far yet.