The conformal grid is large or small depending on the arc length velocity of the parameterization along that section of the curve. Near the pinch point the velocity approaches zero.
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Elliptic curve y² = 4x³ - ax + 1 and its conformal neighborhood for a∈[2,4]. The curve transitions from one component to two at a=3. It is parameterized here with the elliptic functions Weierstrass ℘,℘'. The half period rectangle is shown in light red in the backgroundpic.twitter.com/H5XoDaB9eG
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