The Math Thread

[Vortex]

Well, since a function is also a kind of transformation, you can also graph some fractals in the complex plane. IIRC that is how the Mandelbrot set is made, applying the simple function f(z) = z^2 + c infinite times and painting the resulting function. But when you do that fractals usually have a region that is completely black, that's how you distinguish them from normal functions

[ENIHCAMBUS]

But ain't all numbers complex?

[Vortex]

Depends on what you call a number. But for example quaternions, infinitesimals, transfinite numbers, p-adic numbers, ∞ itself, etc. aren't complex numbers. The definition of fixed point is general, it works everytime there's a transformation. For example, there are fractals made with 3D vectors:



(I dunno why but my body itches whenever I see it )

[ENIHCAMBUS]

Wow, was it made with a 3D printer? Or is just computer generated?

[Vortex]

The wikipedia page says it's raytraced by computer. But raytracing produces very realistic images

[ENIHCAMBUS]

Wow, thats cool!

[The Kakama]

It looks like a moldy rotten thingy. XP

[ENIHCAMBUS]

It looks like a moldy rotten thingy. XP

Thats what I thought first time I seen it! XD

[The Kakama]

https://www.youtube.com/watch?v=JrOG1tKAatg
x^x^x^x... =2
x=sqrt(2)
Recursion can mess with your head sometimes.

[Vortex]

Yep. These kinds of problems are also examples of fixed points, actually

though one has to be careful with those things, as the video comments say. There is another possible solution, x=-sqrt(2), and this one doesn't work, because the iterations don't converge. Usually there are always a pair of solutions, one does converge ("attracting" fixed point), and the other doesn't ("repelling" fixed point).