User:Hans G. Oberlack/sandbox3

Counter-clockwise undulating spiral:

Element	Polynom	0-3 Polynome	Heading
$a_{0}=0+0i$		$0i^{0}+0i^{1}+0i^{2}+0i^{3}$	$h_{0}=1+0i=i^{0}$
$a_{1}=a_{0}+h_{0}=1+0i$	$a_{0}+i^{0}$	$1i^{0}+0i^{1}+0i^{2}+0i^{3}$	$h_{1}=h_{0}\cdot i=i^{1}$
$a_{2}=a_{1}+h_{1}=1+1i$	$a_{1}+i^{1}$	$1i^{0}+1i^{1}+0i^{2}+0i^{3}$	$h_{2}=h_{1}\cdot i=i^{2}=-1$
$a_{3}=a_{2}+h_{2}=0+1i$	$a_{2}+i^{2}$	$1i^{0}+1i^{1}+1i^{2}+0i^{3}$	$h_{3}=h_{2}\cdot i\cdot i\cdot i=i^{5}=i^{1}$
$a_{4}=a_{3}+h_{3}=0+2i$	$a_{3}+i^{5}$	$1i^{0}+2i^{1}+1i^{2}+0i^{3}$	$h_{4}=h_{3}\cdot i=i^{6}=i^{2}=-1$
$a_{5}=a_{4}+h_{4}=-1+2i$	$a_{4}+i^{6}$	$1i^{0}+2i^{1}+2i^{2}+0i^{3}$	$h_{5}=h_{4}\cdot i=i^{7}=i^{3}=-i$
$a_{6}=a_{5}+h_{5}=-1+1i$	$a_{5}+i^{7}$	$1i^{0}+2i^{1}+2i^{2}+1i^{3}$	$h_{6}=h_{5}\cdot i\cdot i\cdot i=i^{10}=i^{2}=-1$
$a_{7}=a_{6}+h_{6}=-2+1i$	$a_{6}+i^{10}$	$1i^{0}+2i^{1}+3i^{2}+1i^{3}$	$h_{7}=h_{6}\cdot i=i^{11}=i^{3}=-i$
$a_{8}=a_{7}+h_{7}=-2+0i$	$a_{7}+i^{11}$	$1i^{0}+2i^{1}+3i^{2}+2i^{3}$	$h_{8}=h_{7}\cdot i=i^{12}=i^{0}=1$
$a_{9}=a_{8}+h_{8}=-1+0i$	$a_{8}+i^{12}$	$2i^{0}+2i^{1}+3i^{2}+2i^{3}$	$h_{9}=h_{8}\cdot i\cdot i\cdot i=i^{15}=i^{3}=-i$
$a_{10}=a_{9}+h_{9}=-1-1i$	$a_{9}+i^{15}$	$2i^{0}+2i^{1}+3i^{2}+3i^{3}$	$h_{10}=h_{9}\cdot i=i^{16}=i^{0}=1$
$a_{11}=a_{10}+h_{10}=0-1i$	$a_{10}+i^{16}$	$3i^{0}+2i^{1}+3i^{2}+3i^{3}$	$h_{11}=h_{10}\cdot i\cdot i\cdot i=i^{19}=i^{3}=-i$
$a_{12}=a_{11}+h_{11}=0-2i$	$a_{11}+i^{19}$	$3i^{0}+2i^{1}+3i^{2}+4i^{3}$	$h_{12}=h_{11}\cdot i=i^{20}=i^{0}=1$
$a_{13}=a_{12}+h_{12}=1-2i$	$a_{12}+i^{20}$	$4i^{0}+2i^{1}+3i^{2}+4i^{3}$	$h_{13}=h_{12}\cdot i=i^{21}=i^{1}=i$
$a_{14}=a_{13}+h_{13}=1-1i$	$a_{13}+i^{21}$	$4i^{0}+3i^{1}+3i^{2}+4i^{3}$	$h_{14}=h_{13}\cdot i\cdot i\cdot i=i^{24}=i^{0}=1$
$a_{15}=a_{14}+h_{14}=2-1i$	$a_{14}+i^{24}$	$5i^{0}+3i^{1}+3i^{2}+4i^{3}$	$h_{15}=h_{14}\cdot i=i^{25}=i^{1}=i$
$a_{16}=a_{15}+h_{15}=2+0i$	$a_{15}+i^{25}$	$5i^{0}+4i^{1}+3i^{2}+4i^{3}$	$h_{16}=h_{15}\cdot i\cdot i\cdot i=i^{28}=i^{0}=1$
$a_{17}=a_{16}+h_{16}=3+0i$	$a_{16}+i^{28}$	$6i^{0}+4i^{1}+3i^{2}+4i^{3}$	$h_{17}=h_{16}\cdot i=i^{29}=i^{1}=i$
$a_{18}=a_{17}+h_{17}=3+1i$	$a_{17}+i^{29}$	$6i^{0}+5i^{1}+3i^{2}+4i^{3}$	$h_{18}=h_{17}\cdot i=i^{30}=i^{2}=-1$
$a_{19}=a_{18}+h_{18}=2+1i$	$a_{18}+i^{30}$	$6i^{0}+5i^{1}+4i^{2}+4i^{3}$	$h_{19}=h_{18}\cdot i\cdot i\cdot i=i^{33}=i^{1}=i$
$a_{20}=a_{19}+h_{19}=2+2i$	$a_{19}+i^{33}$	$6i^{0}+6i^{1}+4i^{2}+4i^{3}$	$h_{20}=h_{19}\cdot i=i^{34}=i^{2}=-1$
$a_{21}=a_{20}+h_{20}=1+2i$	$a_{20}+i^{34}$	$6i^{0}+6i^{1}+5i^{2}+4i^{3}$	$h_{21}=h_{20}\cdot i\cdot i\cdot i=i^{37}=i^{1}=i$
$a_{22}=a_{21}+h_{21}=1+3i$	$a_{21}+i^{37}$	$6i^{0}+7i^{1}+5i^{2}+4i^{3}$	$h_{22}=h_{21}\cdot i=i^{38}=i^{2}=-1$
$a_{23}=a_{22}+h_{22}=0+3i$	$a_{22}+i^{38}$	$6i^{0}+7i^{1}+6i^{2}+4i^{3}$	$h_{23}=h_{22}\cdot i\cdot i\cdot i=i^{41}=i^{1}=i$
$a_{24}=a_{23}+h_{23}=0+4i$	$a_{23}+i^{41}$	$6i^{0}+8i^{1}+6i^{2}+4i^{3}$	$h_{24}=h_{23}\cdot i=i^{42}=i^{2}=-1$
$a_{25}=a_{24}+h_{24}=-1+4i$	$a_{24}+i^{42}$	$6i^{0}+8i^{1}+7i^{2}+4i^{3}$	$h_{25}=h_{24}\cdot i=i^{43}=i^{3}=-i$
$a_{26}=a_{25}+h_{25}=-1+3i$	$a_{25}+i^{43}$	$6i^{0}+8i^{1}+7i^{2}+5i^{3}$	$h_{26}=h_{25}\cdot i\cdot i\cdot i=i^{46}=i^{2}=-1$
$a_{27}=a_{26}+h_{26}=-2+3i$	$a_{26}+i^{46}$	$6i^{0}+8i^{1}+8i^{2}+5i^{3}$	$h_{27}=h_{26}\cdot i=i^{47}=i^{3}=-i$
$a_{28}=a_{27}+h_{27}=-2+2i$	$a_{27}+i^{47}$	$6i^{0}+8i^{1}+8i^{2}+6i^{3}$	$h_{28}=h_{27}\cdot i\cdot i\cdot i=i^{50}=i^{2}=-1$
$a_{29}=a_{28}+h_{28}=-3+2i$	$a_{28}+i^{50}$	$6i^{0}+8i^{1}+9i^{2}+6i^{3}$	$h_{29}=h_{28}\cdot i=i^{51}=i^{3}=-i$
$a_{30}=a_{29}+h_{29}=-3+i$	$a_{29}+i^{51}$	$6i^{0}+8i^{1}+9i^{2}+7i^{3}$	$h_{30}=h_{29}\cdot i\cdot i\cdot i=i^{54}=i^{2}=-1$