Correction to Bifurcation Diagram

In assignment #1 we were asked about the Iterated function system:

x(n+1) = f(x(n))
where f(x) = Cx(1-x), for some range of values for C

I had been coding this incorrectly in mathematica, I recently found out how to code it correctly, and thusly would like to make some corrections to my conclusions about this assignment.
Code:

g[x_] := a x (1 - x);
plist = {};
Do[x = 0.3; Do[x = g[x], {1000}];
Do[x = g[x]; plist = Append[plist, {a, x}], {1000}], {a, 2.8, 4, 10^-2}];
ListPlot[plist];


Approximately what range of C gives you chaos?

• Well as far as I can see the diagram looks more "chaotic" in the darker areas, and less chaotic in the white strips. Upon first look when C <~ 3.48 the graph just looks like a binary tree that keeps branching off two at a time, after that it becomes somewhat of a mess. The diagram does seem to have certain "jumps" though, where it clears up from time to time.

Approximately what range of C does not give you chaos?

• This diagram is definitely not chaotic before C = 3.48. After that it seems like it alternates between chaos and white space. If you zoom in on certain parts, you can see a simlilar pattern to the graph where C <>

Do you see any fractals?

• Yes. I see some self similarity anyway. This leads me to believe that there are fractals in this mapping.

Do you see a connection between chaos and fractals?

• There is obviously a connection between these two things, whenever there are fractals, chaos seems to be lurking around somewhere, be it in the form of randomness (i.e. Brownian motion) or the dark areas that seemingly come out of nowhere in this bifurcation mapping.