You can also see how five copies of the McWorter pentigree fit together by successively adding copies using the buttons below, or by viewing the Lsystem animation farther down.
The scaling factor is still r = 0.381966. This leads to the following IFS [Details]:
\({f_1}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.255} \\
{0.255} & {0.309} \\
\end{array}} \right]{\bf{x}}\)

scale by r, rotate by 36° 
\({f_2}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.254} \\
{0.254} & {0.309} \\
\end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}}
{0.727} \\
{0} \\
\end{array}} \right]\)

scale by r, rotate by 36° 
\({f_3}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.255} \\
{0.255} & {0.309} \\
\end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}}
{0.225} \\
{0.691} \\
\end{array}} \right]\)

scale by r, rotate by 36° 
\({f_4}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.255} \\
{0.255} & {0.309} \\
\end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}}
{0.588} \\
{0.427} \\
\end{array}} \right]\)

scale by r, rotate by 36° 
\({f_5}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.255} \\
{0.255} & {0.309} \\
\end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}}
{0.588} \\
{0.427} \\
\end{array}} \right]\)

scale by r, rotate by 36° 
\({f_6}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}}
{0.309} & {  0.255} \\
{0.255} & {0.309} \\
\end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}}
{0.225} \\
{ 0.691} \\
\end{array}} \right]\)

scale by r, rotate by 36° 
\[\sum\limits_{k = 1}^6 {{r^d}} = 1 \quad \Rightarrow \quad d = \frac{{\log (1/6)}}{{\log (r )}} = 1.86172\]
Angle 36
Axiom F++F++F++F++F
F —>
+F++F−−−−F−−F++F++F−
4 iterations