|
woodlands
Guest
|
 |
« on: October 09, 2006, 07:30:30 PM » |
|
I often wondered if there was another kind of mandelbrot set out there... i have seen many fractal images, but none with the immense complexity of mandelbrot or varients, and especially none with that little bug in the center of it all...i wonder if there is such a set, and if not, why? Is there something fundamental about that image? you would think that there would be a wide variety of such animals, since nature itself is so varied...
|
|
|
|
|
Logged
|
|
|
|
|
rloldershaw
|
|
« Reply #1 on: October 10, 2006, 05:04:27 AM » |
|
Hello Woodlands, I have a possible answer to your question of whether there are other sets that are as complex, or more complex, than the M-set. There appears to be a set that makes the M-set look like a grain of sand on an endless beach. It is the set called nature, which appears to be an infinite set of infinite sets. The set cannot be shown on a computer screen or printed out in its entirety, but you can study the Infinite Fractal Paradigm with your mind's eye at www.amherst.edu/~rloldershaw . Everything manmade is but a toy compared to nature, and we are not too far from a breakthrough in recognizing the amazing discrete fractal infinities of nature. It's a fractal world, Rob |
|
|
|
|
Logged
|
|
|
|
Jules Ruis
Fractal Lover
Posts: 209
Jules Ruis
|
|
« Reply #2 on: October 10, 2006, 09:46:06 AM » |
|
Dear Rob,
Do you know where I can find the indicated complex M-set?
Kind regards,
Jules Ruis.
|
|
|
|
|
Logged
|
|
|
|
|
doncasteel8587
Guest
|
|
« Reply #3 on: October 10, 2006, 01:03:48 PM » |
|
M-Set = mandelbrot-set: Zn=(Zn-1)^2+C
|
|
|
|
|
Logged
|
|
|
|
|
alan2here
Guest
|
|
« Reply #4 on: October 10, 2006, 02:42:05 PM » |
|
nova magnet 1 and 2 barnsley 1, 2 and 3 phenox signed(do a serch in formula's) complex, hypercomplex, 3d ect... mbot sets ect... and there associated julia's If you like mbot but want something new try ajusting the power value's and starting positions www.ultrafractal.com |
|
|
|
|
Logged
|
|
|
|
|
lycium
|
|
« Reply #5 on: October 11, 2006, 04:22:37 PM » |
|
If you like mbot but want something new try ajusting the power value's and starting positions
the very beautiful glynn set is produced via a power of 1.5, and i have some interesting results from mixing julias of various powers (the only example i have online atm though is http://www.deviantart.com/deviation/35013449/?qo=23&q=by%3Alyc&qh=sort%3Atime+-in%3Ascraps - my first 3d "true" fractal, ie, not ray traced l-systems etc). oh and yes, there is definitely something fundamental about the mandelbrot set, just as with the sierpinski triangle - they are called "universal" and can be found everywhere. in fact, the mandelbrot set properly doesn't belong to old benoit, but dates back to the 13th century: http://www.raygirvan.co.uk/apoth/udo.htm |
|
|
|
|
Logged
|
|
|
|
lkmitch
Fractal Lover
Posts: 238
|
|
« Reply #6 on: October 12, 2006, 01:18:46 AM » |
|
I believe the standard Mandelbrot set is the simplest that shows interesting dynamics. Any other quadratic polynomial (like the logistic equation) will give a fractal set with equivalent dynamics, and more complicated formulas will probably yield more intricate structures, particular formulas involving transcendental functions.
I think the "Mandelbrot Monk" is a hoax. While Mandelbrot may not have been the first to discover "his" set (his studies were with z = z^2 - c, anyway), first sightings most certainly don't date back several hundred years.
Kerry
|
|
|
|
|
Logged
|
|
|
|
|
Nahee_Enterprises
|
|
« Reply #7 on: October 12, 2006, 01:56:25 AM » |
|
Thomas Ludwig (lycium) wrote: > > in fact, the mandelbrot set properly doesn't belong to > old benoit, but dates back to the 13th century: > http://www.raygirvan.co.uk/apoth/udo.htm This was a very clever and unique hoax started a while ago, and it seems to be still going around the Internet as if it were the gospel truth.  |
|
|
|
|
Logged
|
|
|
|
|
lycium
|
|
« Reply #8 on: October 12, 2006, 02:31:43 AM » |
|
fooled me for sure :P any ref on the hoax being uncovered? i looked around on the /. article...
|
|
|
|
|
Logged
|
|
|
|
|
|
|
lycium
|
|
« Reply #10 on: October 12, 2006, 06:20:46 PM » |
|
thanks, those are some interesting links  in particular stumbleupon and hyatt's pages! |
|
|
|
|
Logged
|
|
|
|
|
woodlands
Guest
|
|
« Reply #11 on: October 23, 2006, 04:35:48 AM » |
|
If you like mbot but want something new try ajusting the power value's and starting positions [/quote] the very beautiful glynn set is produced via a power of 1.5, and i have some interesting results from mixing julias of various powers (the only example i have online atm though is http://www.deviantart.com/deviation/35013449/?qo=23&q=by%3Alyc&qh=sort%3Atime+-in%3Ascraps - my first 3d "true" fractal, ie, not ray traced l-systems etc). oh and yes, there is definitely something fundamental about the mandelbrot set, just as with the sierpinski triangle - they are called "universal" and can be found everywhere. in fact, the mandelbrot set properly doesn't belong to old benoit, but dates back to the 13th century: http://www.raygirvan.co.uk/apoth/udo.htm[/quote] Thanks, that was beautiful, but its illustrative of my point, in that there is something amazing (and also frustrating) to zoom in on any fractal and either get to just more patterns, or else the mandelbrot figure (what is that referred to anyway?), you know the snowman on its side. i really am surprised that there is just that figure out there. to use an analogy of life, it is like the mandelbrot figure is the soul and everything else is just aura around it. Just surprised there is just this kind of picture, and not anything else. also, the mandelbrot doesnt exist in nature anywhere, just in our mathematical imaginations, although the patterns do exist. I guess the description of what i am looking for is some kind of set that when you are in it, the pattern is just a solid, whereas on the boundry there are hundreds of variations, and that the closer you dig into the boundary, the more complex and beautiful it becomes? |
|
|
|
|
Logged
|
|
|
|
lkmitch
Fractal Lover
Posts: 238
|
|
« Reply #12 on: October 23, 2006, 06:48:05 PM » |
|
i really am surprised that there is just that figure out there. to use an analogy of life, it is like the mandelbrot figure is the soul and everything else is just aura around it. Just surprised there is just this kind of picture, and not anything else. also, the mandelbrot doesnt exist in nature anywhere, just in our mathematical imaginations, although the patterns do exist.
I guess the description of what i am looking for is some kind of set that when you are in it, the pattern is just a solid, whereas on the boundry there are hundreds of variations, and that the closer you dig into the boundary, the more complex and beautiful it becomes?
I'm not sure why you think that the "snowman" is the only thing out there. If you look an other sets, say z 4 + c, then there are other elemental shapes that occur. Maybe it's the case that the snowman is universal like circles are in other fields. And be careful in saying that the Mandelbrot set doesn't exist in nature--it's been found in analyses of magnetic materials and probably in other fields by now. Also, circles don't exist in nature anywhere--they're "just" mathematical models. Kerry |
|
|
|
|
Logged
|
|
|
|
|
woodlands
Guest
|
|
« Reply #13 on: October 24, 2006, 06:14:57 AM » |
|
its been a while, but i thought that when i did a higher multiple, then the heads on the snowman just got more, that somehow the pattern was similar to the snowman, just a little more complex. Does anyone have access or know of how i can get access to plug and play fractal programming? I just have no time anymore, but i really wish i could go exploring again without reinventing the wheel for coding (when i did play with fractals, pre Fractint, i had to teach myself C+ on a 386 with a coprocessor, and did all sorts of tricks to get the screen to show the fractals, and even got to experiment (i think i posted in another topic how i got to imagine a 3rd dimension (an imaginary imaginary axis ), and it worked to actaully draw 3d landscapes (which were cool, but no new snowmen to be found so are there programs that i can use to be able to relatively easily start playing again? thanks a bunch |
|
|
|
|
Logged
|
|
|
|
|
Nahee_Enterprises
|
|
« Reply #14 on: October 24, 2006, 08:44:48 AM » |
|
John (woodlands) wrote: > > Does anyone have access or know of how i can get > access to plug and play fractal programming? > so are there programs that i can use to be able to > relatively easily start playing again? There are hundreds of programs available for use, and the majority or FREEWARE: http://www.Nahee.com/PNL/Fractal_Software.html As to which of them is "relatively easily start playing" with, that all depends on what you wish to do. I personally find most of them easy to use for generating images with. But if you wish to create your own formulae, then there are only a handful that are really good for that ( FractInt is one of the easiest in my opinion). And there are some available at http://www.Nahee.com/Software/ including trial versions of QuaSZ, Fractal Zplot, and Fractal ViZion for creating 3-D fractal images. If you are wanting to actually do some of your own coding, then what language would you prefer to code in?? And which development application/compiler will you be using?? I either have, or know where to find, source code for several coding languages and compilers. |
|
|
|
« Last Edit: April 04, 2010, 06:08:49 PM by Nahee_Enterprises »
|
Logged
|
|
|
|
|
February 20, 2010, 06:04:58 PM
Dilber MC Theme by HarzeM