This one is heavily related to Samsara. Instead of solving for static z₀ seed values (like in Samsara) here we solve for values that have a periodicity of two. This means solving the equation (z²+c)²+c=z. There are a total of four solutions, two of which are the same as in the case of period-1 (to be expected), and two of which are new. When plugging the two new solutions into the z₀ sampler we get the image above.

Now, instead of highlighting the eventual boundary of the main cardioid we end up highlighting the perimeters of the two period-2 lobes of the Anti-Buddhabrot. Faint shadows of the standard Buddhabrot can still be seen around the main feature and are produced when the points finally escape their initial artificial stability. There is also a curious halo of points surrounding the upper lobe whose strikingly ordered patterns seem to emanate from the shiny infinity.

Unfortunately extending this method to larger periodicities would require more complicated root-solving implementations. So to be continued.