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¦