Offset 'cells' from grid of curves

Hi, 

I found a script to create a Phyllotaxy grid pattern on the forum earlier and am having a little trouble manipulating it. 

The grid is formed by a series of spiralling curves and the intersections points have been located. I would like to construct each 'cell' of the grid out of it's border lines so that each cell can be offset. However I'm not sure how to go about breaking down the curves at the intersection points so that they can be rejoined as a single curve that I can then manipulate. 

Attached is the definition, screenshot of the pattern and screenshot of the offset that I want to achieve, as done in Rhino. Any help would be greatly appreciated. 

Tom