This is the shape to represent the demon. It's an autological thing maybe. It is what it represents. The immanent symbol...
You can explore its will for this world by hovering over the diagram above. This is arguably easier to do on a desktop computer. Mobile users can touch but idk how nice of an experience it's gonna be. Sorry
The red function is f(x) = r*x*(1-x)... The grey line is y=x...
The wiki on the logistic map isn't very nice. This is all very simple actually which is why i like it, the wiki does way too much. Read about this kind of diagram though, a cobweb plot.