fractals: the mystery

 https://www.youtube.com/watch?v=POL9wABXBQA

this is mindblowing. i learned about the coastline paradox today, probably three years later than i should have and it is intriguing. fractals are basically shapes or figures of geometry such that the perimeter tends to infinity and the area tends to zero. or the area is basically a fixed quantity, but the line surrounding it can get as jiggly as it wants. like the coastline. 

picture this, you're on mars and looking at the coastline of india. it's literally a dot. you can't even see it. as you get closer it morphs into something more triangular. you calculate it's perimeter approximately. you get even closer. you have to pick up a thread eventually, and touch it to every jagged rock or edge of the coastline. and even then you physically can't measure the exact length of the entire coastline.

it's crazy, no?

that koch snowflake is insanely gorgeous. 

https://www.desmos.com/calculator/acl6xmr9as

this is even more magical. i am filled with this sudden irritatingly mind-numbing desire to LEARN. i don't know why or when or how this feeling invaded my but i want to KNOW. i desperately want to know. that mandelbrot thing is crazy crazy.

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topics to learn:

Dynamical systems

Iteration theory

Chaos theory

Complex dynamics