The configuration that produces the Apollonian gasket requires tangencies among all pairs of seed disks. Here we explore the effect of creating gaps between disks and , and between disks and .¹ In the following program, set nbrLevels to 0. When the controls A gap and B gap are both set to zero, we have the full set of tangencies giving rise to the classic Apollonian gasket. Increasing the value of A gap creates a small gap between the vertically-aligned disks and so that these paired disks are not quite tangent. Similarly, increasing the value of B gap creates a gap between the horizontally-aligned seed disks and .

Increase the value of nbrLevels and vary the values of A gap and B gap to see how these gaps propagate through the figure. Set model to ‘disks’ so that disks get rendered at every level.