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extropalopakettle
No offense, but....
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 Posted: Sat Sep 01, 2012 3:01 pm Post subject: 361 |
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| 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. |
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extropalopakettle
No offense, but....
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| Posted: Sat Sep 01, 2012 4:40 pm Post subject: 362 |
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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. |
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The Potter
Feat of Clay
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| Posted: Mon Sep 03, 2012 4:42 am Post subject: 363 |
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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. |
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The Potter
Feat of Clay
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| Posted: Tue Sep 04, 2012 12:49 am Post subject: 364 |
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The Potter
Feat of Clay
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| Posted: Thu Sep 06, 2012 12:56 am Post subject: 365 |
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This one is a metaphor for the struggle between good, evil, and the circus. |
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itisally*
Guest
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| Posted: Thu Sep 06, 2012 2:34 am Post subject: 366 |
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| Call me crazy, but that is the one I like best! |
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The Potter
Feat of Clay
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| Posted: Thu Sep 06, 2012 11:46 pm Post subject: 367 |
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All good people are a little crazy. |
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Jedo the Jedi
Paragon in Training
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| Posted: Fri Sep 07, 2012 12:34 am Post subject: 368 |
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Getting a little bit more creative, eh?
_________________
Paragon Tally: 19 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting. |
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The Potter
Feat of Clay
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| Posted: Tue Sep 11, 2012 3:14 am Post subject: 369 |
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Actually, less creative. It is just easier and more enjoyable to tweak the colors these days. |
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The Potter
Feat of Clay
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| Posted: Tue Sep 11, 2012 11:39 pm Post subject: 370 |
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This next series explores one little area... |
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The Potter
Feat of Clay
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| Posted: Fri Sep 14, 2012 12:33 am Post subject: 371 |
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Daily projects are fun. Soon I will be able to turn these image into 366 cards and have a calendar  |
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The Potter
Feat of Clay
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| Posted: Tue Sep 18, 2012 1:42 am Post subject: 372 |
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I have always been fond of the "saw blade" areas of the M-set. |
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The Potter
Feat of Clay
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| Posted: Tue Sep 25, 2012 11:44 pm Post subject: 373 |
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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! |
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The Potter
Feat of Clay
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| Posted: Wed Sep 26, 2012 10:29 pm Post subject: 374 |
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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. |
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The Potter
Feat of Clay
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| Posted: Mon Oct 01, 2012 3:17 am Post subject: 375 |
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So what is the meaning of life? |
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The Potter
Feat of Clay
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| Posted: Fri Oct 05, 2012 12:18 am Post subject: 376 |
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How would you behave if you knew someone could watch your every action and you were confined to three rooms? |
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The Potter
Feat of Clay
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| Posted: Sun Oct 07, 2012 12:45 am Post subject: 377 |
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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? |
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extropalopakettle
No offense, but....
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The Potter
Feat of Clay
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| Posted: Tue Oct 09, 2012 1:38 am Post subject: 379 |
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Yes, I have. Very stunning. But Mandelbrot has a very unique shape... |
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The Potter
Feat of Clay
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| Posted: Thu Oct 11, 2012 12:22 am Post subject: 380 |
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Hmm I don't have much to say today. |
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The Potter
Feat of Clay
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| Posted: Sat Oct 13, 2012 3:14 am Post subject: 381 |
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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 |
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The Potter
Feat of Clay
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| Posted: Wed Oct 17, 2012 5:30 pm Post subject: 382 |
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From -0.763904989 - 0.092255806 i
It is strange to get news about GL members via Facebook. |
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The Potter
Feat of Clay
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| Posted: Fri Oct 19, 2012 1:34 am Post subject: 383 |
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From -0.76390479 - 0.09225586 i
The area that I am exploring is so tiny and yet so vast. |
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The Potter
Feat of Clay
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| Posted: Wed Oct 24, 2012 7:15 am Post subject: 384 |
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From -0.763905278 - 0.092256734 i
Today's message is paid for by the committee to create productive groups. |
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The Potter
Feat of Clay
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| Posted: Thu Oct 25, 2012 6:13 am Post subject: 385 |
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From -0.763912002 - 0.092257982 i
I looked around but the shadows were dark and subtle. |
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Jedo the Jedi
Paragon in Training
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| Posted: Thu Oct 25, 2012 11:34 am Post subject: 386 |
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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. |
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Buzzsaw
Newbie Guidance Counselor
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| Posted: Thu Oct 25, 2012 12:17 pm Post subject: 387 |
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Just saw this post. Zag's wife, excellent work on the quilts! (my mom is into the art of quiltmaking)
Very creative! |
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Zag
Unintentionally offensive old coot
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| Posted: Thu Oct 25, 2012 8:15 pm Post subject: 388 |
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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. |
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The Potter
Feat of Clay
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| Posted: Fri Oct 26, 2012 1:50 am Post subject: 389 |
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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. |
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Jedo the Jedi
Paragon in Training
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| Posted: Fri Oct 26, 2012 2:06 am Post subject: 390 |
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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. |
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The Potter
Feat of Clay
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| Posted: Fri Oct 26, 2012 5:30 am Post subject: 391 |
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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. |
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The Potter
Feat of Clay
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| Posted: Sun Oct 28, 2012 5:45 am Post subject: 392 |
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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. |
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The Potter
Feat of Clay
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| Posted: Tue Oct 30, 2012 7:35 am Post subject: 393 |
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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. |
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The Potter
Feat of Clay
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| Posted: Wed Oct 31, 2012 1:40 am Post subject: 394 |
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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. |
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The Potter
Feat of Clay
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| Posted: Thu Nov 01, 2012 4:36 am Post subject: 395 |
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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. |
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The Potter
Feat of Clay
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| Posted: Fri Nov 02, 2012 4:46 am Post subject: 396 |
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A white octopus
_________________
Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy. |
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potter*
Guest
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| Posted: Sat Nov 03, 2012 5:33 am Post subject: 397 |
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Is this fractal real??nah, it is mostly in the imaginary plane |
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The Potter
Feat of Clay
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| Posted: Sun Nov 04, 2012 5:05 am Post subject: 398 |
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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. |
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The Potter
Feat of Clay
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| Posted: Mon Nov 05, 2012 6:59 pm Post subject: 399 |
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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. |
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Legion
Daedalian Member
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| Posted: Mon Nov 05, 2012 10:10 pm Post subject: 400 |
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| I'm a bit sick of fractals now, they're so full of themselves |
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