Is non-admissible

\[1 \rightarrow 2 \rightarrow 4 \rightarrow 5 \rightarrow 6\]

contains a non-fixed periodic branch point

\[\theta = \frac{12}{31}\]

\[1 \rightarrow 2 \rightarrow 5\]

using CairoMakie, BrotViz, Mandelbrot
fig, ax = embeddedtreeplot(12//31)
fig

contains a branch point between the critical point and the critical value which is periodic and non-characteristic

\[1 \rightarrow 2 \rightarrow 6 \rightarrow 11\]

contains two characteristic cycles

\[1 \rightarrow 3 \rightarrow 7\]

\[\theta = \frac{19}{127}\]

fig, ax = embeddedtreeplot(19//127)
fig

has beta and minus beta attached to a non-leaf

\[\theta = \frac{5}{31}\]

fig, ax = embeddedtreeplot(5//31)
fig

Has preperiodic branch points

\[\theta = \frac{2}{9}\]

Has branch points which map to a non-characteristic periodic point before a characteristic point

\[\theta = \frac{7}{19}\]