## Bifurcation Diagram

Generating the famous fractal, which can be used to model populations with various cycles, generate pseudo-random numbers and determine one of nature’s fundamental constants, the Feigenbaum constant $\delta$.
The fractal nature comes from iteratively applying a simple function, $f(x) = \lambda \cdot x \cdot (1-x)$ with $0 \leq \lambda \leq 4$, and looking at its poles.
The resulting image looks mundane at first, when looking at $0 \leq \lambda \leq 3$, though the last quarter section is where the interesting things are happening (hence the image below only shows the diagram for $2 \leq \lambda \leq 4$).
From $\lambda = 3$ on, the diagram bifurcates, always doubling its number of poles, until it enters the beautiful realm of chaos and fractals.

For more on bifurcation, fractals and $\delta$, I refer to this Wikipedia entry and WolframMathworld.

# Python 2.7.7 Code
# Jonathan Frech, 24th of March 2017

## Sierpinski TIrangle

Using the same method used in my previous Sierpinski Triangle program, which is written in Python, I wrote a fractal generator for my graphing calculator TI-84 Plus in BASIC.

"// TI-84 Plus BASIC Code"
"// Jonathan Frech 25th of April, 2016"
"//         edited 21st of May  , 2016"