They are awesomely beautiful.
It's called the Julia set. No explanation why that name. It's gorgeous.
And this gem:
Mind bender. I love it! Have never seen anything quite like that -- and the colors, wow.
http://tinyurl.com/9ofya
Full Version: Fractals Are Groovy
Check it out
They are awesomely beautiful.
It's called the Julia set. No explanation why that name. It's gorgeous.
And this gem:
Mind bender. I love it! Have never seen anything quite like that -- and the colors, wow.
http://tinyurl.com/9ofya
They are awesomely beautiful.
It's called the Julia set. No explanation why that name. It's gorgeous.
And this gem:
Mind bender. I love it! Have never seen anything quite like that -- and the colors, wow.
http://tinyurl.com/9ofya
Fractals are amazing ... just to a search for Mandelbrot on Google images 
While not necessarily a fractal, check out the computer generated
image in this article of the first few moments of a star undergoing a
supernova. Nature is quite the artist.
Stellar Sound Waves Set Off Supernovas
http://www.space.com/scienceastronomy/0602..._supernova.html
Massive, dying stars vibrate like giant speakers and emit an audible hum before
exploding in one of nature's most spectacular blasts, scientists say.
image in this article of the first few moments of a star undergoing a
supernova. Nature is quite the artist.
Stellar Sound Waves Set Off Supernovas
http://www.space.com/scienceastronomy/0602..._supernova.html
Massive, dying stars vibrate like giant speakers and emit an audible hum before
exploding in one of nature's most spectacular blasts, scientists say.
In a desperate attempt to connect this subject with "unmanned spaceflight"....
Over a decade ago, when Mandelbrot was all the rage, I tried writing a program on my home computer to duplicate the slow zoom-in animations into the Mandelbrot set. I figured I'd set starting coordinates on a wide view, ending coordinates on the zoomed-in point (I think it was Horseshoe Valley), and just divide by the number of frames to animate. (Very low resolution--this was an 8086!) Well, it wasn't until hours later that I saw how that looked: very slow start, then faster and faster until we reached the end at dive-bombing speed, exactly like moon impact movies. Ranger 10 to Mandelbrot!
One of those cases where you slap your forehead saying, "Of COURSE it would work that way!", but not realize it until you actually do it. That wasn't the animation I wanted, of course. After thinking, I realized the trick was to reduce each frame's coordinates by a fixed percentage of the current coordinates. (A differential, I now realize, now that I know calculus better.)
I suppose a neat project one day would be to re-time the Ranger descents into a smooth zoom instead of a crash.
Over a decade ago, when Mandelbrot was all the rage, I tried writing a program on my home computer to duplicate the slow zoom-in animations into the Mandelbrot set. I figured I'd set starting coordinates on a wide view, ending coordinates on the zoomed-in point (I think it was Horseshoe Valley), and just divide by the number of frames to animate. (Very low resolution--this was an 8086!) Well, it wasn't until hours later that I saw how that looked: very slow start, then faster and faster until we reached the end at dive-bombing speed, exactly like moon impact movies. Ranger 10 to Mandelbrot!
One of those cases where you slap your forehead saying, "Of COURSE it would work that way!", but not realize it until you actually do it. That wasn't the animation I wanted, of course. After thinking, I realized the trick was to reduce each frame's coordinates by a fixed percentage of the current coordinates. (A differential, I now realize, now that I know calculus better.)
I suppose a neat project one day would be to re-time the Ranger descents into a smooth zoom instead of a crash.
The first time I saw and instinctively recognized a fractal was before (probably) Mandelbrot coined the term!
I had (still have somewhere) the "Aeronautical Chart and Information Center" Ranger 9 Lunar map set made from the nested images that that spacecraft took as it plunged to destruction in Alphonsus Crater.
The first 2 of 5 charts showed the crater at low and high resolution... the 3'rd through 5'th chart showed progressively closer and closer patches of the crater's cratered floor.
What I recognized as "significant" in some way was that though the details were different, the 3 maps looked essentially almost the same. The cratered highland material Imbrian plains are a classic self-similar fractal terrain over a considerable range of resolutions.
I had (still have somewhere) the "Aeronautical Chart and Information Center" Ranger 9 Lunar map set made from the nested images that that spacecraft took as it plunged to destruction in Alphonsus Crater.
The first 2 of 5 charts showed the crater at low and high resolution... the 3'rd through 5'th chart showed progressively closer and closer patches of the crater's cratered floor.
What I recognized as "significant" in some way was that though the details were different, the 3 maps looked essentially almost the same. The cratered highland material Imbrian plains are a classic self-similar fractal terrain over a considerable range of resolutions.
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