Trinoid

$\displaystyle f$	$\textstyle =$	$\displaystyle {1\over(\zeta^3-1)^2}$	(1)
$\displaystyle g$	$\textstyle =$	$\displaystyle \zeta^2$	(2)

$\displaystyle x$	$\textstyle =$	$\displaystyle \Re\left[{{r e^{i\theta}\over 3(1 + r e^{i\theta} + r^2 e^{2i\the... ...\theta}-1)\over 9} + {2\ln(1 + r e^{i\theta} + r^2e^{2i\theta})\over 9}}\right]$	(3)
$\displaystyle y$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 9}}\Im\left[{{-3re^{i\theta}(1+re^{i\theta})\... ...-1} \left({1+2re^{i\theta}\over\sqrt{3}}\right)\over r^3e^{3i\theta}-1}}\right]$	(4)
$\displaystyle z$	$\textstyle =$	$\displaystyle \Re\left[{-{2\over 3} - {2\over 3(r^3 e^{3i\theta}-1)}}\right],$	(5)