title: Control alpha blending / opacity of n overlapping areas
body: <p>I struggle to understand (and control) the blending of alphas - unfortunately, alpha values don't simply "add up" (0.5 + 0.5 is not 1). But how could I achieve that?</p>
  
  <p>The aim is to define the (absolute) grey value of overlapping areas relative to the total number of observations. <strong>See example below.</strong></p>
  
  <p>I tried to set <code>scale_alpha(range = c(0,1))</code> to no avail, maybe I did not use it correctly. </p>
  
  <pre><code>library(ggplot2)
  library(ggforce)
  
  grid_df = data.frame(x = c(1:2, 2.5), y = rep(1,3), r = 1)
  
  ggplot()+
  geom_circle(data = grid_df, mapping = aes(x0 = x,  y0 = y, r = r), alpha = 0.33, fill = 'black') + 
    coord_fixed() 
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/wdObi.jpg" rel="noreferrer"><img src="https://i.stack.imgur.com/wdObi.jpg" alt="enter image description here"></a></p>