No More Self-Intersection:
Here, the lower segment has straightened out in the smooth case (left) forming a "C"-shaped curve. In the polyhedral case, the lower right-hand corner is still being straightened out (and will continue to, right up to the final level), and the center of the "C" is already beginning to be pushed out at the upper right.

[Right] Level 8: The final circle
[left] Level 6: After the critical level
[Left] Comparison to Kuiper's level sets
[Up] Other pictures

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8/10/94 dpvc@geom.umn.edu -- The Geometry Center