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 L-system 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