This time we’re gonna talk about things I know a little bit more about : bifurcation diagrams and iterated functions. The code is available here
Bifurcation diagrams show the behavior of a function $ f: \mathbb{R} \rightarrow \mathbb{R} $, with a real parameter under iteration. Iteration simply means “plugging the output into the input”: a feedback if you will. Iterating from a “seed” $p$, the function can converge to a value (i.e. a fixed point), explode into $\infty $, or go into a cycle. A cycle can have a period, which is the number of iteration you need to do to come back to the original value. In other words, a periodic point $p$ of period $k$ is defined as $f^k(p) = p$, with $k$ being the smallest integer with which this condition is true. Here, $f^k$ simply means iterating the function $k$ times.
On this second episode of “what has Epsilon done for the past years”, we’re gonna talk about… Prime Numbers. Code is available here.
The primes does have this capacity to create some interesting looking things, I’ll give them that. The Gaussian integers are simply complex numbers whose real and imaginary part are integers, and whose modulus is prime. If one component of this number p is 0, then p is prime only if the other component is prime and p % 4 = 3.
This post is the first part of an attempt at explaining most of the small animations I have done in the past few years.
The Ulam Spiral is fairly straight forward: by arranging the integers in a spiral, and only marking the primes, you obtain strange, and frankly cool looking patterns.
Creating this sort of image is very simple. I simply created a basic loop that construct the spiral, which follows the following pattern: ULDDRRRUUUULLLL…, assigning an integer to each step and checking if it was prime.
I’m a Computer Engineer, specialised in Machine Learning and Computer Vision. Most of my research works centers around automated detection in Archaeology. I have introduced the use of YOLO in LiDAR detection for this purpose, in a research internship at the University of Leiden. I have also worked in rare event detection in train borne systems at the SNCF. I am currently available for hire.
