/sci/ - Science & Math

I found this famous image that shows how the logistic map and Mandelbrot set map onto each other showing that the points of period doubling on the logistic map correspond to the "gap" between the mandelbrot circles.

I checked if this picture is accurate in reality. So first I got the ratio between the period-2 and period-4 intervals of the logistic map based on numbers anon gave, that number turned out to be 4.75. Then I got the ratio between the diameters of the largest and second largest black circle in the Mandelbrot fractal which, based on this picture, should be the same ratio. But that number turned out to be 4.23. Those ratios are not even close to each other even though they should be (regardless if one image is scaled or stretched). So what is the deal with this or did I do something wrong?

Used this as source for the other number: https://users.math.yale.edu/public_html/People/frame/Fractals/MandelSet/MandelScalings/CompDiam/CompDiam.html

>>11425117
It feeds back to itself making it SELF-SIMILAR and that's attractive to our brains possible because it requires less resources to process and just right amount of change to become interesting.

>>11260862
The issue must be that they are sending away finite matter from Earth.
Don't pretend this should not be a highly prioritized issue now when private businesses are leaving orbit.

Where did the set exist before computers started looking at it?

>>9566314

>>9456955
It could still work but the system would not be very simple.

Then can you prove a theorem establishing a lower bound on the complexity of the system necessary as a function of the complexity of the source of the input?

So in a sense the logistic map is a slice of the Mandelbrot through the real axis, right? What about all the uncountably many other maps? How do they look? Any renders of them?

>>8618898

I'm just another retard who saves cool pictures, but there's a wiki link:

https://en.wikipedia.org/wiki/Mandelbrot_set#Basic_properties

>>8091119
there are better images to use