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The top row shows a standard double bubble of equal volumes, and a nonstandard cluster in which one bubble is a torus, forming a waist around the other. I created these images to illustrate the proof of the equal-volume case of the Double Bubble Conjecture by Hass and Schlafly in 1995.
The bottom row shows a standard double bubble of unequal volumes (consisting of three spherical caps meeting at equal 120-degree angles), and a nonstandard bubble of the same volumes, in which the larger region is broken into two components (one a tiny ring around the other region). I created these images to illustrate the proof of the general Double Bubble Conjecture by Hutchings, Morgan, Ritore and Ros in 2000.
In all four cases, the cluster is a surface of revolution. More details about the geometry of the examples with unequal volumes, including pictures of the generating curves, are available here online.