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Smarties: Pointy Heart | by gadl
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Smarties: Pointy Heart

Here it is, a circle-to-heart-with-a-tip conformal mapping. The original picture is here.

The complex transformation z↦ z²+2z maps the unit circle into a cardoid (yieding that picture)

The complex transformation z↦ 1-√(1+z) maps the unit circle into a teardrop.

The above picture is a combination of both.

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Uploaded on October 22, 2006