Bifurcation Diagrams

[GrassyGnoll]

It's my final hour in my school's math team and I'm gonna go out with a bang. For the last two years I've been one of the four juggernauts on our Math Bowl team but this time I'm branching out into chalk talks.

My plan for a sick proof is a coordination of the bifurcation diagram, fractals, and logistic equations. Problem is, I know jack nothing about bifurcation. Any helpful mathematicians clear on the links between the three?

[GrassyGnoll]

Disregard that, I'll just do a derivation of the Taylor Series and talk it up a bit.

[Jorkens]

Totally irrelevant to Taylor's Theorem or Bifurcation Diagrams, but this is quite fun, don't know if it helps any:
http://www.ics.uci.edu/~eppstein/junkyard/euler/