Mandelbrot Fractal Zoom: rainbow island twists
by iamafractal
2:31 - 67,849 views

If you want to support my art, go to http://zazzle.com/kliman* and buy some stuff based on my art!

I have been exploring the Mandelbrot fractal since the mid 1980s. I'm fascinated by the concept that no matter how far you go, there's always more.

The problem with exploring its infinite depths though, is that as you go deeper, and as the images get more and more complicated, the amount of computer time needed to see further increases exponentially. The first frame was not zoomed in at all, and took only a fraction of a second to calculate. The last frame in this partial work, though, which is zoomed in 2^308th times, compared to the first frame, took 11 days on a dual core 2.8Ghz PC. The frames from 2^309th to 2^335th (10 Googles or 10 with 101 zeros after it) are taking really really long, but one day, we'll get to see what is in there.

Dr. Stephen Wolfram once said:

"If the whole history of our universe can be obtained by following definite simple rules, then at some level this history has the same kind of character as a construct such as the digit sequence of pi. And what this suggests is that it makes no more or less sense to talk about the meaning of phenomena in our universe as it does to talk about the meaning of phenomena in the digit sequence of pi."

My interpretation of that is that since pi is an infinite series of digits, every single thing we know, is in pi. Your phone number, my phone number, a perfect jpg picture of you, one of me, and everybody else, your genome, my genome, the entire universe, another one of our universe, but with one little thing different, and all the other possible universes too. But that doesn't just happen in pi. It happens in e too. and it happens in the mandelbrot fractal. A mathematician once said that any system could be encoded into the form of any other system, so really, it's just a matter of how you decode what you are looking at and what part of it you decode.

By looking at the Mandelbrot set the way we do here, we see what we see here, as, what John Conway once told me, is merely an artifact of the way we observe it, as is the case with reality itself.

Here are some interesting phenomena to observe in the Mandelbrot fractal in general, and in this journey in particular.

*wherever you are, the image is made up of little copies of itself, as well as copies of what you would see if you zoomed out a bit. often you can see a complete synopsis of your location by looking at the details in a picture.

*there are an infinite number of miniature Mandelbrots to be found inside the Mandelbrot fractal. Each is identical to the original that you see before you zoom in, except that it is also surrounded by whatever was around it.

*as you approach one of these miniature Mandelbrots, you can observe first a doubling of what was around it, then a doubling of that, and then another doubling, until finally as you approach the event horizon, an infinite number of whatever was surrounding that Mandelbrot in the first place.

*that means if you find something that looks just like a sea horse, and zoom into it in the right spot, you will find a Mandelbrot with sea horses around it. If you find spikes, you will find Mandelbrots with spikes around them. If you find spirals, you will find Mandelbrots with spirals around them.

*each of the Miniature Mandelbrots inside a spiral is surrounded by the view of that spiral from where the miniature Mandelbrot is. What I mean by that is if the spiral is infinite, which it is, then if you zoom in to the 12th loop of that spiral, you will find miniature Mandelbrots surrounded by 12 loop spirals.

*if you zoom in to a very tightly wound spiral, there will be tightly wound spirals around the miniature Mandelbrots inside. These tightly wound objects take far more computational power to visualize because they have rapidly increasing iterations towards their infinitely deep centers.

*everything as you zoom in further is additive, so if you first find a Mandelbrot with seahorses, then go to a spiral nearby that miniature Mandelbrot, it will be just like the spiral that would have been in the corresponding spot in the main Mandelbrot, except that it will also have seahorses juxtaposed.

*no matter how many things you add together this way, as long as you properly calculate the colors so that you can visualize what you're seeing, it all fits together perfectly.

Zoom created with Fractal Extreme by Cygnus software.

-Jan 1, 2009

Doctor Who Theme Tune 2005-2007 By Murray Gold
by moonraker79
2:37 - 5,986,768 views

Doctor Who Theme Tune 2005-2007 By Murray Gold