Paige McLoughlin’s Reviews > Chaos and Fractals: New Frontiers of Science > Status Update

Mandelbrot sets and their relation to Julia sets. They are connected and generated by very similar methods.

the strange attractor which has chaotic orbits that neither repeat nor are predictable but stay in a certain range. The Lorentz attractor for example can be constructed from a handful of partial differential equations that can't be cleanly solved but makes just such a strange attractor that has chaotic orbits but in a certain well definite range in 3-dimensional space.

Period doubling as a route to chaos and Feigenbaum number that expresses the proportions to that doubling. Behold another video.

https://www.youtube.com/watch?v=ovJcs...

Randomizing fractals and power spectra with Brown, White, Pink, and Black noise. Fun stuff I am fascinated with the fact that there are different flavors of randomness that obey different distributions of statistical noisiness. I love when something that seems like one thing from far away turns out to be many things up close.

I love the Mandelbrot set so easy to generate simply points on the border between contained and escaping to infinity of complex numbers added and squared over and over again. The equation for people into that is C(n+1)= (C(n) + K)^2 over and over again. I will drop a video here. https://www.youtube.com/watch?v=NGMRB...
https://www.youtube.com/watch?v=FFftm...

space-filling curves

going into the gory details of actually building fractals via specific iterative methods.