Status Updates From Chaos and Fractals: New Fro...

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...

Deterministic Chaos (Butterfly effect) and the mixing or folding analogy for how it comes about mathematically

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.

an empirical method of figuring out fractional dimensions in box-counting methods that work for objects in the real world presented to the observer.

Hausdorf measures and measuring fractional dimensional freaks that seem to populate actual existing reality we have here.

Math and nature love to iterate. We are all constructivists now.

This is cool I get new insights (incites) every time I read it,

This is a perfect book for a voraciously curious but very undisciplined mind. Good stuff.

intro examples in chapter one the Sierpinski gasket, The multiple copier machine copy, shrink, twist (repeat) nature does that a lot. The logistic iteration and deterministic chaos and butterfly effect and fun with Fibonacci's rabbit sequence and how it tends to the golden ratio. All the hits are in the first chapter.

found the other big doorstop of a book I enjoy so much. Scribble scribble,