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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...

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

Dear Rob,

Do you know where I can find the indicated complex M-set?

Kind regards,
Jules Ruis.

M-Set = mandelbrot-set:  Zn=(Zn-1)^2+C

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

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

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

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.    :D

fooled me for sure :P any ref on the hoax being uncovered? i looked around on the /. article...

Thomas Ludwig (lycium) wrote:
>
>   fooled me for sure :P any ref on the hoax being uncovered?
>   i looked around on the /. article...

There are several places on the Internet that talk about this particular webpage, which Ray Girvan created for an "April Fool's Day" joke.  Just using a quick search with Google, using the words "udo.htm" and "hoax" will show several links to go to, such as:
      http://www.massey.ac.nz/~wwifs/mathnews/Nzms82/news82.htm#monk
      http://www.tjhsst.edu/~dhyatt/supercomp/n106.html
      http://www.stumbleupon.com/url/www.raygirvan.co.uk/apoth/udo.htm
Or you can write to Ray Girvan <ray@raygirvan.co.uk>, <info@raygirvan.co.uk>, <ray.girvan@zetnet.co.uk> and get it directly from him.

thanks, those are some interesting links :) in particular stumbleupon and hyatt's pages!

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?

I'm not sure why you think that the "snowman" is the only thing out there.  If you look an other sets, say z⁴ + 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

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

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 (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 (http://www.fractint.org/ftp/) is one of the easiest in my opinion).  And there are some available at http://www.Nahee.com/Software/ (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.
 

If you wish to create and use your own formular and do other experiments then also the Fractal Imaginator (Fi) is a very good program.

See: http://www.storesonline.com/site/1265859/product/205-5160684

I'm not very good at math, but isn't it "formula", with no r on the end?  Or have you coined a new word: "formular" with a special application?

With apologies,
Rob

Dear Rob,

I am Dutch, so my English language is full of errors. You are completely right: 'Formula' is the correct word.

Thanks.
Jules.

thanks for the info.  i coded back then in C+, but have gotten out of it, and embarased to say that i code in Access basic for database applications mainly, and basic is pretty lousy for math applications.  Let me try some of these tools, see if they can help me explore

John (woodlands) wrote:
>
>    thanks for the info.   ......
>    Let me try some of these tools, see if they can help me explore

You are more than welcome!!  If you need specific assistance with any of the fractal applications you decide to try out, then either post a message here to get help from somebody or send me a private email.

>
>    i coded back then in C+, but have gotten out of it,
>    and embarased to say that i code in Access basic
>    for database applications mainly, and basic is pretty
>    lousy for math applications.

VBA can do quite a bit within the Microsoft Office products.  I have coded hundreds of thousands of lines of code for not only Access, but Excel, Word, Outlook, etc...  But none of those is the correct development environment for creating fractal applications.

You should think about acquiring Visual Studio so that you can work with both C and Basic.  Both of them will allow you to create whatever you want in the way of a fractal app.  Microsoft's Basic can do many things now that it never could before and is very much compatible (as far as functionality is concerned) with C+ and C#.

compatible yes, but performance?  I remember watching fractals draw dot by dot until i moved to C+, and got satisfactory performance  (on a 386 remember :) 

actually isnt there some story about the orignal mandelbrot guy (benoit ole bean himself) waiting so long for the next set to show up that he tried to calculate the percent differnce between sizes or something, and came up with a constant or  some such?  4.3 or somthing?

John (woodlands) wrote:
>
>    compatible yes, but performance?  I remember
>    watching fractals draw dot by dot until i moved
>    to C+, and got satisfactory performance....

Back then, C was quite a bit faster, but these days, Basic has gotten much better and C has become a bit slower in my opinion.  I think it is because Microsoft keeps adding so much to C (like they do the Office Suite) that it is becoming bloat-ware.

But if you really want a lot of speed in execution, then you should really program in Assembler.

on the contrary, c/c++ speed has just been getting better and better over the years (more features doesn't mean anything gets slower unless the slow ones are actually used, obviously), and basic still lags behind even delphi and is on par with java for some types of computation last time i checked.

what's more, it's almost impossible to beat a good c/c++ compiler these days with assembler programming; you have to have an incredibly directed attack in mind (eg very specific simd optimisation plans), spend hours and hours and hours fine tuning it to a specific architecture, and even then you'd still be very lucky to beat it. i used to program optimised triangle rasterisers in x86 assembler back in the (mode 13) day, and stopped after things got crazy with the pentium2. out-of-order cpu architectures mean you can never really know when stuff gets executed, it's all optimised internally anyway. i know totally incredible asm programmers who've been doing it for decades who still only manage par with gcc 4.2, doing sse code in a very restricted context.

the other thing is that with the current trend towards parallelism you really don't want to be writing threading code in assembler. my dualcore amd runs at 2.5ghz (5ghz effectively) pretty much day and night computing fractals, and i don't think a 2x speed improvement with asm over c++ will ever be found again...

to wit, i just rendered a 12288x8192 "julius ruis" set with 256 samples per pixel in under a minute with really casual code, about 30 minutes from start to finish including the (much more subtle) image-to-palette routine: http://www.fractographer.com/propaganda/tlset.png (warning, that image is huge in dimensions and filesize: 12.3mb)

all that hard core programmingspeak makes me afraid, very afraid :)

John (woodlands) wrote:
>
>    all that hard core programmingspeak makes me
>    afraid, very afraid  :)
>
>    Does anyone have access or know of how i can get
>    access to plug and play fractal programming?   .....
>    (when i did play with fractals, pre Fractint, i had to
>    teach myself C+ on a 386 with a coprocessor.....
>
>    i coded back then in C+, but have gotten out of it,
>    and embarased to say that i code in Access basic for
>    database applications mainly.....

Well, if you are really wanting to do your own "plug and play fractal programming", then as you already know (based upon your statements about actually doing programming), you have to learn to speak the language.    ;)

But if you do not have the time to invest in such tasks, then I suggest just downloading one of the many FREEWARE and TRIALWARE fractal generators that are available, and just do some image (and optionally formula) creation.

And besides, with the hundreds of available programs already out there, why would you really want to do your own fractal programming??  Much more fun seeing what various graphics can be produced.     :)

>Well, if you are really wanting to do your own "plug and play fractal programming", then as you already know (based upon your statements about actually doing programming), you have to learn to speak the language.    ;)

yep, i do know the world of coding, and as such its actually not the fear of the programming itself, its the time involved...getting to know a program is usually some intense effort to make it play nice.  thankfully, i guess  there are more plug and play things out there...but from experience, as soon as you want to do somethign different, its a tougher ballgame.  For instance, i want to imagine a third axis (pun intended, what could be more imaginary than the imaginary axis), and code accordingly.  i did do it once when i had programmed in C, and it was cool, but it involves generating a third loop to scan through for the third axis, plus inventing the third parameter (i.e. a +bi +cj) and its arithmetic...(a+bi+cj)(a+bi+cj)=(a**2 - b**2 +c**2 -b*c) + 2abi +2acj   (the idea is that i*i=-1;    j*j=1;    i*j=-1 ) 

so in my ignorance of the plug and play programs, i fear that they wouldnt be able to handle that particular quest for unusual fractal worlds, or some other ways i want to play, and my time is so bad right now that even typing into forums is a stretch :(  damn real world!

plus hearing the other computer speak of how people who really know the stuff and use things to optimize the calculations really makes me roll my eyes.  ah well, maybe i will get time to investigate and make things happen in spite of my reticence for starting.   :)

actually, back to the original question, are there other fractal forms out there that could be considered as complex as mandelbrot, or with an atomic core like the snowman, but different?  Every other form i see just appears to be variations of the "aura", which never zoom in to see anything other than more aura, or a core that is  different than the mandelbrot "set".  anyone have examples?

thanks, its fun to be talking about this stuff.