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.

Bifurcation Diagram lambda in range [2; 4]
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

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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.

Faintly visible Somewhat visible Strongly visible

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

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