The Critical Level:
This is the critical level, formed by a saddle point (arrow), where two lobes of the level curve come together, join at a point forming an "X", and then separate in the opposite direction. In this case, the two left-most segments in the "X" come from one lobe and the two right-most ones from the other lobe; when they separate in the next step, the two upper lines of the "X" will form a lobe, as will the two lower ones. This can be seen in the sequence shown below:

[Right] Level 6: After the critical level
[left] Level 4: Adding the triple point
[Left] Comparison to Kuiper's level sets
[Up] Other pictures

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