Shahin's Eclectic Weblog

Chaotic Systems and Randomness

This experiment fundamentally questions randomness as it proves you can mimic any random sequence of numbers (i.e. a sequence of head/tails on a coin) using a chaotic system once the proper initial conditions are derived and fed into the chaotic system. The question then is what is random? Here, we load a random sequence of zeros and ones, then take the chaotic recursive system X[i+1] =4 X[i] (1 - X[i]) and find the appropriate initial condition that will produce the same sequence. To view the Mathematica file click here.

It would also be a good exercise to verify data compression applications using this method. Theoretically, the initial conditions may require more accuracy than the generated sequence for an unknown or derived initial condition (Kolmogorov: A sequence is random if the only algorithm for generating the sequence requires as many bits to describe)

Paper based on some of my research

This paper is about analysing the data from the probes orbiting the planet Mars.  To read the paper click here:  Download Engineering_Masters_Research_Paper.pdf

 

MIT Open CourseWare

MIT, one of the world's top universities, has placed all the material for 500 courses on the Internet. They have placed everything on their web site in a move to provide a free educational resource to everyone around the world. Visit the web site at: http://ocw.mit.edu/index.html

Is there an ocean in space?

I became interested in whether Jupiter's moon Europa has a sub-surface ocean. I wanted to compare the surface on Europa to frozen ice on Earth's oceans. You can get to the research paper if you click on the image of Europa below:

After this research I wanted to understand the mathematics behind combining two fractals so I took a fractal's class and the results are also posted under "super-imposing fractals" in this weblog.

Super-imposing Fractals

If two distinct processes create two differing fractal dimensions (i.e. geological processes--breaking of ice and shifting of icy surfaces) then what happens if the processes get super-imposed? What is the mathematics involved in this? The math attached is perhaps one way to try to answer this. I used both empirical (Mathematica tm) and theoretical approaches yielding similar results.

Fractal Dimension and Crystalline Formations

A paper comparing crysltalline formation and fractal growth.

Craters Chains and Comets

Some research on crater chains.