escaping set

I had hoped there'd be more interest in this. I guess I'm the only one alone on Christmas.

Usually for the Mandelbrot set you use:

Re(c) = x
Im(c) = y
z = c
for i = 1 to number_of_iterations
z = z² + c
next
if z -> infinity, it's part of the escaping set, else it's not

where z & c are complex

Anyway, it's used to define the geometry of certain fractals. But if you use this instead:

z = (z ^ 4) + c

You'll get a triangle fractal.

Using z = (z ^ 5) + c, you'll get a 4-pointed star, etc.

When you see the pattern, you can backtrack and realize the Mandelbrot set is like a star with a single point, and it's not dot. There's also a 2-pointed star with an unusual shape.

I forgot to mention, (x,y) is the location of the point being plotted, and number_of_iterations can be an arbitrary positive number, with higher values giving a more detailed image. I find 17 iterations to work well.

Anyway, the thought crossed my mind, why can't we use a similar technique for describing physical objects? Like, say, I don't know, black holes? They seem to have a pretty well-defined geometry beyond which things tend to infinity. What do you think?

Well, I guess it's not a popular topic around here. I suppose I should just get drunk, what with it being a holiday.

Merry Christmas.

Most individuals who view this site have an intellect comparable to that of a monkey. Without the ability to visual the fractal sets described by the equations it is hard to blame them for not paying attention. Maybe some pictures or videos would help explain things.

It's already widely accepted that Mandelbrots are the natural way to geometrically transcribe our world. Being applicable to a black hole would be purely theoretical. Without a hands on investigation to test the theory, it would just be anothing chip in the lunch box...

Algebra was first period man, sorry did learn much, Was stoned

^^^^^^^^^^This^^^^^^^^^^^^^

Get out much?

How dare you attempt to ridicule someone because they know something you don't. Shame on you for being suck a fuckhead.

"suck a fuckhead?"
wtf
:jackiechan:

Typo.

set666

GLP is fucked up tonight

As opposed to what other night?

oh shit. it is not night, it is morning..When did that slide around???

Something must be going on. I can't type worth shit. I think I have everything correct before I post but nope, I should begin to proofread.