Free boundary minimal surfaces of genus zero

The critical catenoid is conjectured to be the unique embedded free boundary minimal surface with genus zero and two boundary components in the three-dimensional Euclidean unit ball. Even more challenging would be a rigorous classification of all embedded free boundary minimal surface with genus zero and more than two boundary components. The images below are a first attempt at visualising all such surfaces with up to 8 boundary components.

Free boundary minimal surfaces of genus zero with 3, 2 and 1 boundary components

Free boundary minimal surfaces of genus zero with 4 boundary components

Free boundary minimal surfaces of genus zero with 5 boundary components

Free boundary minimal surfaces of genus zero with 6 boundary components

Free boundary minimal surfaces of genus zero with 7 boundary components

Free boundary minimal surfaces of genus zero with 8 boundary components

Free boundary minimal surfaces of genus zero with many boundary components