I’ve been busy at work designing square #1. Here is one tentative design:

It is a bit too busy, but I kind of like it. I may add a circle of plain muslin around the edges of the brain-like inner design, to give the eye a place to rest amidst all the ruffling.
I thought I’d share a couple of the things that didn’t work, and why I didn’t like them:

This is the outer ruffle on its own. By itself, it’s too plain and the circle in the center is too large (IMO) to make an interesting design on its own. You could set up several circles – which is what was done in the original – but on the whole it needs something to add variety.

This doesn’t work. I had hoped that adding a square grid would break up the unity of the circles a little bit, and add a little spice, but the contrast is too strong, jarring in fact.
Next I tried a more circular pattern, this one a twelve-sided polygon which approximates a circle:

This doesn’t work either. The contrast is not as jarring as the squares, but the triangles still clash with the circles-and-radiating-spokes theme in the ruffle.
So then I thought of putting a piece that would riff with the radiating spokes – take them to the next level, as it were:

This I liked much better. The radiating spokes pick up the radiating lines of the ruffle, but are more disciplined in appearance, adding variety without disturbing the unity of the circle motif.
However, I felt that there still wasn’t enough variety in the piece. All those radiating circles related just a bit too much.
So I added the “brains”:

This broke up the radial symmetry just enough to give the design a focal point.
Anyway, I’m not wedded to this particular design yet, I think it needs more work. I may get rid of the ruffle, or else make it a double ruffle, like this:

…and generally I’m not super-satisfied with it. I want to play with the design some more.
However, since I actually want to start handling fabric sometime in the very near future (my hands are twitching!), I think I will start making at least some of the components of the design. I may totally redesign it on the fly, once I’ve created a ruffle and a yo-yo and some other stuff.
I’ve pretty much given up on making the quilt a unified design. I don’t want to have to plan that far in advance – this is a side project (at least for now) and not my main focus. So I may just wind up with a bunch of sample squares that don’t “go together”. That would be fine, too.
I do want to play with color, too – so I will be dyeing at least some of the fabric. I’ve decided to use silk, as I have a lot of small pieces of white silk to use up, and because I can dye it with acid dyes. Dyeability with acid dyes is handy because it means I can dye pieces very quickly – a few seconds in the microwave – and then iron them dry, which is useful if you are an instant gratification bunny like me. I don’t want to have to wait 24 hours to try out a new color! With acid dyes, I can have it almost instantly.
The other advantage of using silk is that I have everything from stiff bridal satin to soft organza in my stash (the legacy of haunting Exotic Silks’ remnant bins for awhile). So I can try a lot of different fabric textures without having to buy anything new!
Remember, there is such a thing as a crazy quilt. It seems to me that that is what you are designing more than a regular quilt. From what you’ve done before, I think a crazy quilt would appeal to you more than a regular quilt anyway.