thomas

Today I dove into how the Mandelbrot set is constructed, and I am awestruck by the simplicity of it.

I knew that chaotic, nonlinear systems could be elegantly simple under the hood, but this takes the cake.

The ability to zoom infinitely into this gorgeous fractal landscape using just one second-degree polynomial is mind-blowing

This is the ELI5 video that sold it for me — they didn’t even refer to complex numbers!

PhD in aviation ∩ climate science | Aviator, diver, ETH maxi, nexialist | Host of /diving /ethfinance /eth-staker /geopolitics /science /singapore /thomas

This is the ELI5 video that sold it for me — they didn’t even refer to complex numbers!

https://youtu.be/7MotVcGvFMg

Physicist, quant, & Art Deco advocate |                                        

Moderating /science and /artdeco |     

instagram.com/johncamkiran

Thanks John! I thought the M set was also computationally irreducible. Is there a way to figure out for which values of c the z^2 + c iterations will remain bounded, without actually doing the calculations? (within the trivial bound of 2 that is)

Not to detract from the beauty of this set, but I did want to note for the readership that such ‘closed-form’ solutions are quite rare in the study of chaotic phenomena. Most such systems are what Stephen Wolfram calls ‘computationally irreducible’, meaning that the only way to find out what happens at some time (in this case, zoom) is to sequentially compute all that which came before it.