You know what? Forget about modifying individual tiles. Users
can modify individual pieces after rendering.

Here's the general concept for dynamics:

1. (Double?-)Click on any other tile besides the base tile.

(note: although the frame look empty, they will be considered 
filled objects when selecting and modifying, so you don't have 
to pick the edges). 

2. Modify the angle, size etc. of that tile by dragging its transform
handles. Move the tile for shifting. The corresponding values of
all the other tiles in the render frame will also automatically be 
modified via some sort of interpolation. (may take some time to 
render, but since they're just frames it shouldn't take too long)

3. Use Ctrl- drag handles to constrain to row values.
Shift- drag to constrain to column values.
For radial tiling, they'd be constrained to angular and radial values.

4. Alt-drag the same handles to add jitter: drag right to add, 
drag-left to remove.

So now the only dynamics still needed in the toolbar are
trace + Blur, Opacity, Hue, Saturation and Lightness.
BOHSL will appear as tools, a bit like tweak tools. Just drag
over any frame with it after selecting it with double-click.
The ctrl, shift and alt modifiers still apply.

(same as last mail:)
http://postimage.org/image/4235075wd/

The "result" will be "visible" thanks to that little sphere in the
corner.

And hopefully we're a step closer to stuffing a 7-tabbed dialogue
into one toolbar!

Jasper: I only saw your reply after I finished this current one. 
I'll remove the unclump button (besides, fuse tile renders 1 object,
and I think the normal tiling can be made to render just a normal
group of objects, so you can just ungroup).

I can also consider your "gradient" approach. Basically render
frame will come with two reference tiles which will be connected
to the base tile with a line (to look a bit like a gradient line).
You can move it to another tile, but they will still be constrained
to row/column. So, you modify these two tiles specifically.

This would save up the use of a few modifiers. I think I'll put up 
a mock-up for each and ask again which one people prefer.

The interface will likely be more complicated for P3 transformation
and such. Then again, I never did understand how "rows and
columns" worked for those. : (