fractals

As I said in my last post regarding the section in which we were discussing Brownian motion, I was working on using mathematica to graph an ...

In assignment #1 we were asked about the Iterated function system: x(n+1) = f(x(n)) where f(x) = Cx(1-x), for some range of values for C I h...

For the past couple weeks in class we have spent a lot of time discussing (and trying to prove) Brownian motion and it's characteristics...

Problem number 1) from the syllabus page of the website is stated as 1) Consider the iteration , x(n+1)=f(x(n)) , where f(x) = Cx(1-x) , ...

This fractal is similar to a Cantor set. It has no overlaps and comes from the map of the union of two transformations f and g. This is the...

This assignment was stated as follows: Consider the chaotic iteration x(n+1)=f(x(n)) , where f(x) = 4x(1-x) , and initial condition x(0)= ...

This was a tough one. I feel like everything that has to do with fractals is very ambiguously defined. Even the definition of a fractal se...

Yesterday, class was spent discussing how a fractal was filled. This was a very interesting lecture that helped me understand more how frac...

The better part of today's class was spent proving a theorem, which after a little bit of search I found is called the "Banach Fixe...

Back on the 10th, we were given the assignment to find the value of 3 different sums (series). The first of which was the sum of (1/(2^i)) a...