Power of the crowd

Figure 1.  The rules

Figure 2.  An example

Figure 3.  The graphs of $ f_n $ for $ n = 4 $ (blue), $ n = 3 $ (orange)

Figure 4.  The graphs of $ f_n $ for $ n = 3 $ (blue), $ n = 5 $ (orange), $ n = 7 $ (green) and $ n = 9 $ (red), onk__ge $ [0,1] $ and $ [0,{}^{1}\!\!\diagup\!\!{}_{5}\;] $

Figure 5.  The graphs of $ f_n $ for $ n = 2 $ (blue), $ n = 4 $ (orange), $ n = 6 $ (green) and $ n = 10 $ (red)

Figure 6.  $ \frac{1}{4}-w_n $

Figure 7.  $ f^\prime_{2n}(\alpha_{2n}) $ for $ n $ in $ [2,250] $

Figure 8.  The graph of $ f_2 $

Figure 9.  The graphs of $ f $ for $ p = {}^{1}\!\!\diagup\!\!{}_{2}\; $ (blue), $ p = {}^{1}\!\!\diagup\!\!{}_{4}\; $ (orange), $ p = {}^{9}\!\!\diagup\!\!{}_{10}\; $ (green)

Figure 10.  The graphs of $ f_n $ for $ n = 7 $ (blue), $ n = 9 $ (orange), $ n = 11 $ (green)