Inversion

Recursive circle packings generated by reflection in circles. Every arc you see is one seed circle, pulled back through the group.

Construction
Reflect in the dual circles instead of the seeds, so the recursive circles that fill the gaps are drawn — the actual Apollonian gasket, not just the seeds and their nested images. Apollonian mode only, no shape or mirror, single precision.
Seed circles3
Tangency1.000
Rotation0°
Seed circles
Drag a centre to move it, drag the rim mark to resize. A filled swatch reflects points that fall inside; a hollow one reflects points outside.
Mirrors
Order k6
Wedge angle0°
Dimension
Seed tetrahedron
Tangency gap0.0000
Sphere radius1.000
Light52°
Drag to orbit, wheel to move in and out. Radius 1.000 is the mutually tangent case, where the enclosing sphere satisfies the 3D Descartes relation exactly. The camera stays inside the enclosing sphere, since from outside you only see its shell. The orbit reflects in the dual spheres and measures distance to the seeds, which is what makes the packing fill the gaps rather than nest inside the seeds.
Generator shape
Exponentcircle
Shape angle0°
Inversion in a superellipse instead of a circle: 1 is a diamond, 2 is exactly the circle, high values approach a square. Only the circle is conformal, so shaped generators drop to single precision and lose the deep-zoom range.
Iteration
Reflection depth90
Arc weight1.10
Halo0.00
Samples1×
Resolution100%
Coordinate precision
Single-precision loses the picture past about 3 000×. Auto switches to an emulated double there, which costs roughly 5× the frame time and holds to about 1010×.
Colour
Mapped from
Cycle1.00
Shift0.00
Fill strength0.90
Curvature
Scroll to zoom, drag to pan. H handles · R randomise · F fit · S save.