Lyapunov Exponent of Logistic Map

Calculating the Lyapunov Exponent of a Time Series (with python code)

(In a later post I discuss a cleaner way to calculate the Lyapunov exponent for maps and particularly the logistic map, along with Mathematica code.) I found this method during my Masters while recreating the results of an interesting paper on how some standard tests for chaos fail to distinguish chaos from stochasticity (Stochastic neural network …

Continue reading Calculating the Lyapunov Exponent of a Time Series (with python code)

Python Script to Generate Frequency Counts of Words in a Text

The following python script takes a text file as input and produces an unsorted list of frequency counts of words in the text as an output text file. It's pretty simple and short, and uses only the regular expressions module re of python, which is a standard library, so this script will run in any …

Continue reading Python Script to Generate Frequency Counts of Words in a Text

Locating Numbers inside Bisected Interval Sequences

I think in a real analysis course in the second semester of my first year, the teacher was discussing the nested interval theorem, when one of his examples or something he was saying struck me, and I thought of this interesting problem. Well, interesting to me. We pick any fraction, say. Now we look at …

Continue reading Locating Numbers inside Bisected Interval Sequences