There are several means of building set of tangent circles. One of them is called an Apollonian Gasket: it recursively fill the space between tangent circles. But this method leaves large empty spaces inside the initial circles. The idea is then to fill again those empty circles with the same algorithm, changing some parameters to induce some randomness and get some surprise at the end.

Another means is called the Steiner Chain: putting a chain of tangent circles between two circles.

It is easy to construct 2D stars as closed polyline with constant angle between the segments. But what about 3D stars? I tried to construct 3D stars using the same angle between adjacent segments and between two planes spanned by three adjacent segments. Indeed for specific angles closed polylines can be found in 3D-space forming interesting shapes. Also I varied the sequence of the direction of plane rotation when stepping from one segment to the next one.

Images exposed in this gallery were generated using a simple program based on polar coordinates in two dimensional plane. All other variables which appear in formulas are generated and taken out of the current process. The results are more or less symmetrical with no high level of complexity.

Landing page: Gallery French

Constrained Willmore surfaces in 3-space