Pastelland Forum

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

But ain't all numbers complex?

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 )

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

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

Wow, thats cool!

It looks like a moldy rotten thingy. XP

The Kakama wrote:It looks like a moldy rotten thingy. XP

Thats what I thought first time I seen it! XD

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

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).