The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

 Fractals Revived Goto page 123456789101112131415161718 Previous  1, 2, 3 ... 9, 10, 11 ... 16, 17, 18  Next
Author Message
extropalopakettle
No offense, but....

 Posted: Sat Sep 01, 2012 3:01 pm    Post subject: 361 The amazing thing about the Mandelbrot set is that the math is actually fairly simple ... amazingly simple in light of the amazing complexity of what it produce. A program do draw the Mandelbrot set can be written in a very few lines of code.
extropalopakettle
No offense, but....

Posted: Sat Sep 01, 2012 4:40 pm    Post subject: 362

This is a very high level, but complete description of the algorithm

 Code: for real numbers X in range -2 to 2 do following {    for real numbers Y in range -2 to 2 do following    {       assign complex number C the value X + Yi       assign complex number Z the value 0 + 0i       repeat following until distance between Z and 0+0i > 2       {          assign Z the value Z^2 + C       }       if above loop never ends,          complex number C is in the Mandelbrot set, so          color point (X,Y) black       otherwise,          color point (X,Y) a pretty color depending on          how many times the loop iterated    } }

Now, in practice, "if above loop never ends" would be something like "if it executes more than MAX times".

And in practice, we like to "zoom in" on "microscopic" details of the Mandelbrot set, and examine smaller areas, so we restrict X and Y to smaller ranges.

And in practice, the value of MAX needs to be increased when zooming in on the edge of the Mandelbrot set to get an accurate picture.

But that is it.

[edit: oh, and of course "for real numbers X in the range ..." means some subset of them ... they get mapped to the rendered image's pixel's X coordinates ... and similarly for Y]

I coded this in 1985, when Scientific American first popularized the Mandelbrot set, and know the above by heart (they never explained how complex numbers map to points on the plane ... which is obvious to me now, but wasn't then). Amazingly, the executable (I no longer have the source) can still be run on windows, putting the screen in a 16 color 640 by 480 graphics mode. It allows zooming in. It also does a recursive rectangular subdivision of the screen, capitalizing on the fact that if the border of an area of the image is all one color, the entire area will all be that color.
The Potter
Feat of Clay

 Posted: Mon Sep 03, 2012 4:42 am    Post subject: 363 The real/complex plane is something that took me years to digest before I understood it. But today it seems so very simple. The "real" part is left/right and "imaginary" part is up/down. My simple explanation of the M-set: We are looking at one complex point at a time, the form of A 1 + B 1 i and then squaring it and adding C. C= A 0 + B 0 i I methodically write it like this: (A 1 + B 1 i)(A 1 + B 1 i) + C And then it goes to A 1 2 + 2AB 1 i + B 1 2 i 2 + A 0 + B 0 i We take the i 2 and turn it to (-1) and move real and imaginary parts together... (A 1 2 -B 1 2 + A 0 ) + (2AB 1 + B 0 )i And just define A 2 and B 2 so we have basically what we started with A 2 + B 2 i. And check to see if (A 2 2 +B 2 2 )^0.5 > R. When it doesn't, keep "squaring + C" forever. Most of time, R=2. Today R=0.95, which causes the M-Set to be discontinuous.
The Potter
Feat of Clay

 Posted: Tue Sep 04, 2012 12:49 am    Post subject: 364
The Potter
Feat of Clay

 Posted: Thu Sep 06, 2012 12:56 am    Post subject: 365 This one is a metaphor for the struggle between good, evil, and the circus.
itisally*
Guest

 Posted: Thu Sep 06, 2012 2:34 am    Post subject: 366 Call me crazy, but that is the one I like best!
The Potter
Feat of Clay

 Posted: Thu Sep 06, 2012 11:46 pm    Post subject: 367 All good people are a little crazy.
Jedo the Jedi
Paragon in Training

 Posted: Fri Sep 07, 2012 12:34 am    Post subject: 368 Getting a little bit more creative, eh?_________________Paragon Tally: 19 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.
The Potter
Feat of Clay

 Posted: Tue Sep 11, 2012 3:14 am    Post subject: 369 Actually, less creative. It is just easier and more enjoyable to tweak the colors these days.
The Potter
Feat of Clay

 Posted: Tue Sep 11, 2012 11:39 pm    Post subject: 370 This next series explores one little area...
The Potter
Feat of Clay

 Posted: Fri Sep 14, 2012 12:33 am    Post subject: 371 Daily projects are fun. Soon I will be able to turn these image into 366 cards and have a calendar
The Potter
Feat of Clay

 Posted: Tue Sep 18, 2012 1:42 am    Post subject: 372 I have always been fond of the "saw blade" areas of the M-set.
The Potter
Feat of Clay

 Posted: Tue Sep 25, 2012 11:44 pm    Post subject: 373 I like to think of our universe could be flattened into "somewhere in the Mandelbrot Set". Technology allows us to know about other tiny worlds and also much bigger worlds. Yet we really don't know how impossibly small or large things can be. The amazing part is that it is all connected!
The Potter
Feat of Clay

 Posted: Wed Sep 26, 2012 10:29 pm    Post subject: 374 I am curious if anyone else ever explored the world of fractals. I render these at 768 x 576. I would love to see other people's creations.
The Potter
Feat of Clay

 Posted: Mon Oct 01, 2012 3:17 am    Post subject: 375 So what is the meaning of life?
The Potter
Feat of Clay

 Posted: Fri Oct 05, 2012 12:18 am    Post subject: 376 How would you behave if you knew someone could watch your every action and you were confined to three rooms?
The Potter
Feat of Clay

 Posted: Sun Oct 07, 2012 12:45 am    Post subject: 377 After going to a quilt show today (the joys of living with your mother again) I feel that someone needs to make a nice Mandelbrot quilt. What sort of effort would be required to make the pattern?
extropalopakettle
No offense, but....

 Posted: Sun Oct 07, 2012 12:59 am    Post subject: 378 You've seen these? (by Zag's wife) http://www.greylabyrinth.com/discussion/viewtopic.php?p=509308#509308 http://zag.net/quilts/kaliedoscope1/
The Potter
Feat of Clay

 Posted: Tue Oct 09, 2012 1:38 am    Post subject: 379 Yes, I have. Very stunning. But Mandelbrot has a very unique shape...
The Potter
Feat of Clay

 Posted: Thu Oct 11, 2012 12:22 am    Post subject: 380 Hmm I don't have much to say today.
The Potter
Feat of Clay

 Posted: Sat Oct 13, 2012 3:14 am    Post subject: 381 From -0.763909042 - 0.09225444 i Ah, I see the new glpics doesn't replace files with the same name. Dum de dum Last edited by The Potter on Wed Oct 17, 2012 5:31 pm; edited 1 time in total
The Potter
Feat of Clay

 Posted: Wed Oct 17, 2012 5:30 pm    Post subject: 382 From -0.763904989 - 0.092255806 i It is strange to get news about GL members via Facebook.
The Potter
Feat of Clay

 Posted: Fri Oct 19, 2012 1:34 am    Post subject: 383 From -0.76390479 - 0.09225586 i The area that I am exploring is so tiny and yet so vast.
The Potter
Feat of Clay

 Posted: Wed Oct 24, 2012 7:15 am    Post subject: 384 From -0.763905278 - 0.092256734 i Today's message is paid for by the committee to create productive groups.
The Potter
Feat of Clay

 Posted: Thu Oct 25, 2012 6:13 am    Post subject: 385 From -0.763912002 - 0.092257982 i I looked around but the shadows were dark and subtle.
Jedo the Jedi
Paragon in Training

 Posted: Thu Oct 25, 2012 11:34 am    Post subject: 386 Do you crop these a certain way on your own? Couldn't you display a different part of the fractal? I only ask because I saw those 3-D ones extro posted, and they make the camera zoom around and give you a tour._________________Paragon Tally: 19 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.
Buzzsaw
Newbie Guidance Counselor

Posted: Thu Oct 25, 2012 12:17 pm    Post subject: 387

 extropalopakettle wrote: You've seen these? (by Zag's wife) http://www.greylabyrinth.com/discussion/viewtopic.php?p=509308#509308 http://zag.net/quilts/kaliedoscope1/

Just saw this post. Zag's wife, excellent work on the quilts! (my mom is into the art of quiltmaking)

Very creative!
Zag
Unintentionally offensive old coot

 Posted: Thu Oct 25, 2012 8:15 pm    Post subject: 388 Thanks! I'll let her know. she just had two quilts accepted into a national show: http://zag.net/quilts/dragon/ and http://zag.net/quilts/bargello2/ and you can see more of her quilts from here: http://zag.net/ (plus I'll be putting some other pictures up, probably this weekend.) BTW, the first of those two that are entered into the show has already won first prize in a smaller, local show.
The Potter
Feat of Clay

 Posted: Fri Oct 26, 2012 1:50 am    Post subject: 389 From -0.763906984 - 0.092250728 i The images are effectively cropped or framed to make the composition interesting to me. The area outside my images is frequently "boring". I don't have an easy way of zooming (outside the software) or showing more than I want to.
Jedo the Jedi
Paragon in Training

 Posted: Fri Oct 26, 2012 2:06 am    Post subject: 390 That's cool. I was just affirming that what we are seeing is what you have chosen to show us. I guess that makes it artistic. _________________Paragon Tally: 19 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.
The Potter
Feat of Clay

 Posted: Fri Oct 26, 2012 5:30 am    Post subject: 391 From -0.763911445 -0.092253495 i Yes, it is art The process consists of finding an interesting area and then finding a color scheme that is pleasing. Getting the colors right is usually the more difficult part of the process._________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Sun Oct 28, 2012 5:45 am    Post subject: 392 From -0.763911063 -0.092251556 i Mmmm spiraly_________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Tue Oct 30, 2012 7:35 am    Post subject: 393 From -0.763906544 -0.092256341i I am not sure why colorsets are usually hard to work with._________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Wed Oct 31, 2012 1:40 am    Post subject: 394 From -0.763958833 -0.092469204i Reds and blues are much easier._________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Thu Nov 01, 2012 4:36 am    Post subject: 395 From 0.34271879+ 0.42987121i And now for something different!_________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Fri Nov 02, 2012 4:46 am    Post subject: 396 A white octopus_________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
potter*
Guest

 Posted: Sat Nov 03, 2012 5:33 am    Post subject: 397 Is this fractal real??nah, it is mostly in the imaginary plane
The Potter
Feat of Clay

 Posted: Sun Nov 04, 2012 5:05 am    Post subject: 398 This area is very Julia-like but it still comes from the Mandelbrot set._________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
The Potter
Feat of Clay

 Posted: Mon Nov 05, 2012 6:59 pm    Post subject: 399 The large areas are very "flat" and then bottleneck down and transition to another "flat" expanse._________________Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.
Legion
Daedalian Member

 Posted: Mon Nov 05, 2012 10:10 pm    Post subject: 400 I'm a bit sick of fractals now, they're so full of themselves
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersAarondalfAdrithAnonymousBicho the InhalerBuzzsawCeltChuckCourkdoormouse11Dragon PhoenixElethiomelextropalopakettlegroza528itisallyi_h8_evil_stuffJack_IanJedo the JediL'lanmalLegionLucky WizardMackayMarvinmathgrantMatthewMatthewVNeocortXNsofOne Skunk ToddPorroQuailmanSamadhiScurraSessieStained GlassStuieThe PotterTraviswordcrossZagzorT Kitty Oldest FirstNewest First
 All times are GMTGoto page 123456789101112131415161718 Previous  1, 2, 3 ... 9, 10, 11 ... 16, 17, 18  Next Page 10 of 18

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum