In the previous program, the four seed disks are known as kissing Schottky disks since each seed disk touches the two disks comprising the other pair, forming a chain of tangencies. But it’s not necessary for the seed disks to kiss, and in the following program they kiss only for the value .

As explained on the previous page, every disk represents a composite transformation . Applying to ‘s three noncancelling seed disks produces three new disks nested inside , a process we refer to as expanding disk . You can see this in action by clicking a disk in the program. Set model to ‘spheres’ and click any sphere to expand it. Whereas only highest-level spheres are rendered, disks at every level are rendered when model is ‘disks’. Since only highest-level disks are not yet expanded, only these can be expanded by clicking.

To program the click-to-expand behavior, every disk has several properties including its composite transformation and the index of its outermost seed disk . To expand disk , apply to each of ‘s noncancelling seed disks. For example, the disk stores the transformation and the index to seed disk . To expand , we apply to the seed disks , , and .