Trip to e214.
The last two minutes are very intense! The final magnification is e.214. Want some perspective? A magnification of e.12 would increase the size of one actual single particle, to the same size as the earths orbit! e.21 would make that particle look the same size as the milky way! e.42 would be equal to the universe! This zoom smashes all of them away. If you were “actually traveling” into the fractal, your speed would be faster than the speed of light.
To download the 10 minute HD version Click Here.
What is a fractal anyway? Well as you asked I will give you a brief run down.This particular fractal is called the Mandelbrot fractal set. The Mandelbrot fractal set is created using a mathematical formula that involves complex (infinite) numbers. These numbers are plotted onto a graph to produce the image. It is named after Benoît Mandelbrot. A famous mathematician who discovered fractal geometry. The boundary of this fractal is infinite. Meaning that when you magnify it, the edge of the boundary eventually becomes infinity complex. Buried within the Mandelbrot set are an infinite amount of smaller sets – that are self similar to the original. This animation is a journey to a set so infinitesimally small that if you could see all of the original it would be bigger than the universe!
the first song of the mix is “oxia – domino”
The second song is “David Amo & Julio Navas – feelings don’t stop”
Christopher
February 11, 2010
@ 5:17 am
Very very beautiful! I just downloaded the large file – very worthwhile use of $5. Our 21-month-old girl is a fractal fanatic. She’ll love this one!
teamfresh
February 11, 2010
@ 5:19 am
aww thanks for taking the time to comment – I’m glad to hear your daughter is a fan!
Alex Bowyer
February 11, 2010
@ 10:43 pm
This is awesome, well done! How did you ensure the zoom centred on an “interesting point” rather than one of the solid areas?
teamfresh
February 11, 2010
@ 10:45 pm
Thanks! As with all my animations I explored manually and once I had found the destination I then started the render aming towards my final destination co-ords.
John W. Ratcliff
February 11, 2010
@ 11:24 pm
When the fractal video gets near the end the morphology of the image changes dramatically from the standard fractal view. Was this a result of any degrading of the mathematical precision in the computation, or is this simply how the equation looks when you delve that deep?
Thanks,
John
teamfresh
February 12, 2010
@ 12:24 am
Thats just how it looks, I had not run out of precision its just that there is so much detail crammed into such a small area that no matter how much the image is anti aliased it will still look “foggy” if the animation carried on travelling towards the boundary then the fogginess would evaporate as the details of the boundary would become clearer.
neko
February 12, 2010
@ 5:17 pm
wow!!!! this is an amazing use of computer power and imagination
thanks for the great ‘trip’
teamfresh
February 12, 2010
@ 6:14 pm
your welcome =)
Erique
February 13, 2010
@ 1:27 am
Great choice of destination. Impressive!
teamfresh
February 13, 2010
@ 2:03 am
why thankyou – I’m glad you approve
Nate
February 13, 2010
@ 5:40 am
Who is the music by? It sounded like Rich Curtis?
foo
February 13, 2010
@ 5:44 am
any chance there’s a link to a free download? or is the money actually going to teamfresh?
Elektro
February 13, 2010
@ 5:50 pm
Nice track selection, there.
Which John Acquaviva track is that? I know I have it, but can’t remember which one…
Andy Brice
February 13, 2010
@ 6:00 pm
I would love to embed this amazing vid on http://www.successfulsoftware.net (with due credit and link back). Is that possible?
teamfresh
February 13, 2010
@ 8:58 pm
ok – in answer to the last 4 posts…
@nate I do not know who the music is by- It was a mix knocked up for me by a dj friend who i am no longer in contact with
@foo If you want a free download then i suggest you rip the video from vimeo using real player,
If you want the high quality version it will cost you a measly $5.00 a percentage of this goes to me (teamfresh) and all proceeds will be ploughed into the running costs of this blog – buying new hardware to create these animations faster and to a higher standard for all you guys – As things stand i am not anywhere near breaking even yet so any donations would be gratefully received, you can donate in two ways
1)buy more animations
2)send payment via paypal to sexy_day100@hotmail.com
@Elektro I have no idea which track it is im afraid
@andy Brice If you wish to embed this animation I suggest using the vimeo version which can be found here
http://vimeo.com/1908224
any links back would be great!
cheers all
teamfresh
Simon
February 15, 2010
@ 4:20 pm
This is terrific! Great job!
The end is really giving me the creeps, the shapes become more and more round and regular, until suddenly the original Mandelbrot shape reappears in the final frames… this thing is crazy!
btw, how did you chose the coordinates you zoom into? Was this intuition?
teamfresh
February 16, 2010
@ 12:13 am
Im glad you like it! =) I wish it was intuition! instead I manually zoomed into the fractal first until I reached that infinitesimally Mandelbrot (that took a while I can tell you!) and then I rendered the zoom afterwards travelling to the same co-ords.
Mgon
February 18, 2010
@ 6:44 am
Way wicked cool.
Gert-Jan
February 20, 2010
@ 1:22 am
Hi, I love this video! It really stretches the mind without having to resort to chemicals
Couple of questions if I may:
Is the mandelbrot shape at the end really the direct result of the formula or did you blend that in for dramatic efect?
If it is real, what do you get when you zoom in on the same bit as you zoomed in on at the beginning.
Really curious about that one, can you jump there and just zoom in?
Do you ‘turn’ the camera? Sometimes things are straight x,y and sometimes at odd angles. Are these angles from the formula or do you turn the camera?
What kind of setup do you use for rendering?
Love your work,
GJ
teamfresh
February 20, 2010
@ 1:56 am
Hey – glad you like the anim – who needs drugs when you have teamfresh
in answer to your questions…
the Mandelbrot shape at the end IS a direct result of the formula, no clever video editing was used!
If you zoomed into the same area as before you would end up hitting even more complex patterns found within the set. The set itself is INFINITELY DEEP! So you could just go on zooming forever as long as you stay on the boundary of the set.
If you know your way around the fractal you could then end up arriving at another one of the infinite amount of smaller Mandelbrot sets that are found within the original. So in short yes you could just “jump” there and then carry on zooming.
want to know more about the mandelbrot set? click this link…
http://www.hd-fractals.com/what-is-the-mandelbrot-set/fractals/446
The only problem that is faced when the set is magnified to this extent (ie: e214) is the amount of time it takes to render each image/frame.
Because the set is calculated using a mathematical formula
- that is made from complex numbers –
the deeper you go the more precision you need regarding the maths.
so e214 is a short way of saying –
there is 214 numbers in the string after the decimal
- ie: 0.56685687967578……..(214 digits)
want to know more about the math? click this link
http://www.hd-fractals.com/mandelbrot-maths/fractals/434#content
you also have to take into account the amount of iterations that are used to create the image. (each iteration is the result of the formula being repeated) so the more iterations you have also affects how long it it takes to calculate.
here is an interesting link to a post i made explaining iterations a little more…
http://www.hd-fractals.com/428/fractals/428#content
In short this means that although I was able to render the very first frame of the animation in a fraction of a second, the final frame took more like 18 hours to render.
As for the camera angle, it is possible to change it – but in this instance I did not. The Mandelbrot set itself is totally 2D although some parts appear to have a three dimensional feel – It is as flat as a pancake, so if you changed the camera angle it would look a bit like google earth when you tilt the camera- it would strech the image but still be flat. Any angles you saw were a direct result of the formula
As for the set up of my rendering – my exact methods are under wraps
but I can tell you that I lovingly create the animations on my beat up laptop
- then I have a separate dedicated machine (running a linux operating system) for the rendering of the animation.
I render all my animations with anti – aliasing. This means that an animation takes longer still to render but in my opinion it is worth it.
Dont know what anti aliasing is? – click this link to find out!
http://www.hd-fractals.com/what-is-fractal-anti-aliasing/fractals/158
hope this helps your curiosity
oceans of love
teamfresh
Meee
February 21, 2010
@ 5:25 pm
Hi!
Excellent video
I’ve seen an other video from you about e214 but it’s only about 5 minutes. Why there are 2 videos of diferent duration?
I love the music of that video but since a few days i cannot play it on vzaar. I know you don’t have the music of the 1′ minutes vdeo but do you have the music of the 5 minutes video?
Thanks a lot!
teamfresh
February 21, 2010
@ 9:01 pm
Hi, I am glad you like the animation
I actually made 4 different versions on the animation in total. I took down the “vzaar” version for bandwidth reasons. The music is a song called “sad robot” and its by “Pornophonique” The same track is also used on “purple haze” you can view it here….
http://www.hd-fractals.com/purple-haze/fractals/animations/425
For copyright reasons and to have the ability to sell my animations legally I paid a licence fee to use that track. If you would like a copy you can do one of two things
1) buy a copy of “purple haze” ($3)
2) go to jamendo and download it for free (personal use only) you can find the whole album it was taken from here….
http://www.jamendo.com/en/album/7505
**although it is free to download the track/album I would ask you to seriously to please make a donation to the artist to encourage them to continue producing music.**
oceans of love
teamfresh
Justin
February 23, 2010
@ 9:13 pm
Kindly explain how could e.42 be equal to the universe. Thanks.
teamfresh
February 24, 2010
@ 11:23 am
The visible universe appears to have a radius of 14 billion light years because the universe is about 14 billion years old. The light from more distant objects simply has not had time to reach us. For this reason everybody in the universe will find themselves at the middle of their own visible universe. The precise scale of the universe is complicated by the fact that the universe is expanding. Galaxies we see near the edge of the visible universe emitted their light when they were much closer to us, and they will now be much further away.
The true size of the universe is probably much larger than the visible universe. The geometry of the universe suggests that it may have an infinite size and that it will expand forever. Even if the universe is not infinite, our visible universe must be a minute speck in a much larger totality
If you describe fractal magnifications in the same way that you do a microscope (for example, 10x, 50x, and 1000x), you quickly find yourself getting into ridiculously large numbers. Whereas microscopes are limited to around a million times magnification, fractal programs frequently use up to a billion, billion, billion, billion times, or more.
Instead of describing magnifications in terms of incomprehensibly large numbers that are very difficult to say,
computer and math wizards in the audience can call it the base two logarithm of the magnification, but we’ll just call it the number of zooms. Conversion of the number of zooms to the magnification is fairly easy. A magnification of one thousand is approximately 10 zooms. A magnification of one million (one thousand thousand) is approximately 20 zooms. A magnification of one thousand million is approximately 30 zooms, and so on.
the zoom in on this fractal is 713 times. this means The magnification of the picture when we did this animation is ten to the 214th power — that’s a one followed by two hundred and fourteen zeros. That’s equivalent to a million times a million times a million times…repeated many times. That’s serious magnification. At that magnification, a wee tiny subatomic particle would appear to be considerably larger than the visible universe! How much larger? Well, it actually only takes about one hundred and forty zooms to make an electron the size of the visible universe, so 713 zooms, is simply an incomprehensibly, outrageously, enormously, ridiculously large zoom level. here is a small chart covering zoom levels…..
Zooms.Magnification. Size of monitor.
8 256 football field
9 512
10 1024 100-story building
20 ~1E6 Vancouver Island
30 ~1E9 Jupiter’s radius
40 ~1E12 Earth’s orbit
50 ~1E15
60 ~1E18 distance to Alpha Centauri
70 ~1E21 Milky Way galaxy
80 ~1E24 large doesn’t cover it!
90 ~1E27
100 ~1E30 huge
110 ~1E33 really huge
120 ~1E36 even huger
130 ~1E39 enormously gargantuan
140 ~1E42 size of electron to the universe
713 ~1E214 incomprehensibly big…but we did it!
760 ~1E228 released to the public in April!!!!!!
hope this helps your curiosity Justin
oceans of love
teamfresh
Meee
February 24, 2010
@ 4:27 pm
:O
!!!!! At last that music! Thank you very much!!!
best animations » Blog Archive » Mandelbrot fractal set trip to e214
February 24, 2010
@ 7:05 pm
[...] created by teamfresh - hd-fractals.com [...]
teamfresh
February 26, 2010
@ 1:25 am
the first song of the mix is “oxia – domino”
The second song is “David Amo & Julio Navas – feelings don’t stop”