Varying the break-off condition when iterating the Mandelbrot set
HTML-код
- Опубликовано: 12 окт 2024
- The Mandelbrot Set is the set of complex numbers c that remain bounded when plugged into the sequence
z_0=0
z_n=z_{n-1} ^2 +c.
Practically that means you keep iterating the sequence until it has a bigger absolute value than a certain boundary, where you are sure it will diverge to infinity. Then you color that number according to how any iteration steps it took you to get there.
After enough iteration steps you give up, assuming the number will never excel the boundary and thus is part of the Mandelbrot Set, so you color it black.
For this to work you must choose a boundary as your break-off condition that is at least 2.
In this viedeo I tune up the break-off condition from 0 to 4. So in the first half of the video we do not see the real Mandelbrot set, because we exlude numbers that are actually part of it.
Music: Beginning of "Algorithms" by Chad Crouch
licensed under a Attribution-NonCommercial License. (Link: www.freemusica...)
This Video is licensed under a Attribution-NonCommercial-ShareAlike License. (creativecommon...)
Interesting twist on rendering the Mandelbrot.
Yeah, I've finally understood how the Mandelbrot set gets his complicated recursion!
Glad we could clear that up! ^^
The Mandelbrot zoom after eating too much brocolli:
You can never eat too much Broccoli!
@@NonEuclideanDreamerlol xd
this happens when you plant a mandelbrot seed
And you eat the Mandelbrot fruit
and you die with it
@@jahabarintos1518and you turn into a Mandelbrot and then u be the most famous
Bro...
This is how the mandelbrot set grows from a seed.
Yeah, nice way to think about it!
or a Mandelbrot Seed.
@@NonEuclideanDreamerand u ate a Mandelbrot fruit
@@NonEuclideanDreamerthen u turn into a Mandelbrot
0:20 perfect
i bet you could stack the slices and make a 3D mandelbrot set!
Yes, that should work.
@@NonEuclideanDreamer you should do that and put it on your instagram!
@@hyperbolictesseract6609 We'll see. I suspect it won't look good without shading and I haven't got around to that yet.
@@NonEuclideanDreamer Well this is the video what happens when you plant a Mandelbrot Seed.
@@chrisrodriguezm13 MANDELFLOWER
One second lemme inflate my Mandelbrot
00:20 this bailout in ultra fractal is 4
in Kalle’s Fraktaler is 2
Maybe it's just a difference of how you look at it: |z|
in mine it was 2000 but now it's 2
I was expecting a jumpscare for some reason
interesting!
I like this in 0:08
I studied mandelbrot set in msc maths. Mandelbrot set is nothing but endless reiteration. Nothing spiritual, supernatural or remarkable.
made by ???
Me.
Krdoodossododoe
This is also called "bailout growing"
What z replace with )
)^2 + C
1
2
Formula:
Initialization Code:
bailout = Any Value
Iteration Code:
z = z2 + c
love mandelbrot crap also whats the song
Thanks! That's Chad Crouch, they have really cool Creative Commons Music. Check out the link in the description!
@@NonEuclideanDreamer crazy that you're still responding to comments after october 2019
@@para3668 what was in october 19?
@@NonEuclideanDreamer upload date lol
Theres a speed issue, but it doesnt matter all that much as long as its reasonably large.
Not sure what you mean.
@@NonEuclideanDreamer If you increase the break off condition you get more colours for your visualization but also a more heavy computation.
@@vizart2045 ah yes. In this code I use the computation from the previous frame for the next, so I don't need a lot more computation for the entire video then for the last frame.
@@NonEuclideanDreamer I was thinking in a more general framework.
|z|>2 is the most efficient condition. But for some Mandelbrot Variations it is difficult to determine.
If C Is Replaced By ꧅, It Is z2 + ꧅.
Wtf
idk? Why?