Just for fun I though I would have a look at some Julia sets with random noise. So I decided to have a look at the Julia set for \(F_{c}= \exp(\frac{z^{2}}{2})\) and \(c = 2- 0.5I\). This was chosen for no particular reason.

To this I modified the algorithm to include some noise in the form of a random complex number. The random number is of the form \(R_{\#} = \frac{z_{R}}{\#}\)

where \(|z_{R}| \leq \sqrt{2}\) and \(\#\) is a real number that scales the random number.

Basically, as the random numbers become larger then the fractal pattern gets “dissolved” in random noise. I won’t claim there is any real scientific value in this experiment. Enjoy the pictures.

Here we have no noise. As the pictures go down the noise increases.

Random thoughts on mathematics, physics and moreā¦