Competition Idea

[jwm-art]

The Real Mandelbrot Competition

This competition has very strict rules:

1) Only images of the Mandelbrot Set are allowed.
2) The only colouring method allowed is the traditional banded method: iterations are mapped to colours.
3) The only post processing allowed is anti-aliasing/sub sampling.
4) Images must be verifiable as part of the Mandelbrot set. To this end, precise locations must be provided with each image.

What the judges should look for:

1) Creative zooming: unusual shapes and forms created by the effects of zooming into the M-set.
2) Images which suggest the image is not a part of the M-set
3) Images which are at very deep depths within the M-set which require arbitrary maths precision.

What does this mean?

It means that beauty is not the sole criteria for this competition. Ugly images are welcome and encourage! It means that beauty is welcome and encouraged, but must also fulfil knowledge of the M-set creatively applied. It means that the images will probably take a long time to render.

Because of these considerations, image sizes may be as small as 400 x 400 pixels, or as large as you feel sensible.

Prizes
My respect!

Any takers?

[edit]
This is something I'd genuinely like to see. I've seen the deep zoom animations on youtube and elsewhere, I've read about how long these things took to render.  I'm curious as to how the final coordinates were chosen? Was it an algorithm that chose them, or did you zoom in with an image generator until you found the coordinates and then made a video zooming to those points? If the latter, which is what I'm hoping, surely you discovered some interesting images along the way? What insights did you glean? Use them!

I admit, that this past week is the first time I've been able to get past the 64bit precision barrier of double precision maths, and so it's still exciting and I'm not sure what to expect. Will what I find live up to my expectations!?!?

[lkmitch]

I think this is a good idea and I'd gladly enter.  One other thing I'd like to see is a short blurb about how/why this particular image was chosen.  If it's just because the contributor likes it, that's fine.  But if there was some definite process/algorithm for finding this zoom, particularly for deep zooms, it would be good if that were shared.

[jwm-art]

Ah good I agree with the blurb about choices made, and the sharing of the algorithm. Although a part of me wants to make it a rule that no algorithms other than wet-ware based algorithms may be used. But maybe that's taking the restrictions too far? I do want to see images that have been thought about, though equally I don't want to discount more impulsive zooms as they can often lead to new insights.

I feel I should justify the tight rules a little. Artists have always used restrictions and limits in what the allow themselves to do, it's as an important aspect in art as is freedom. Particular examples escape me, but practices such as colour palette restriction, the novel where none of the words contained the letter E, etc.

[LesPaul]

2) The only colouring method allowed is the traditional banded method: iterations are mapped to colours.

There is one thing you might want to clarify, for fairness -- does it matter how the iterations are mapped to colors?  I would suggest, at the least, that you allow a logarithmic mapping.  The reason for this is that generally, the more you zoom in, the smaller the color bands get.  Once you get fairly deep, they really don't even look like color bands any more, just random static.  The bands essentially become much smaller than a single pixel in width, so what you see just looks like noise.  But if you use the logarithm of the number of iterations, you get back to nice, smooth color bands.

Many people also prefer the smooth gradients (as opposed to distinct bands) that are produced by "normalizing" the iteration count.  The color bands are really just artifacts of the bailout algorithm used.  Here are images illustrating the difference (from Wikipedia):

Not normalized:


Normalized:

[jwm-art]

The colour mapping of iterations maybe scaled such that a 256 colour palette may be stretched across several thousand iterations with the in-between colours formed by interpolation.

The colour bands may not be replaced by a smooth gradient. This defeats the purpose of exploration and deep zooming. If you want a smooth gradient you only need zoom deep enough. Here is an example:


http://www.fractalforums.com/gallery/?sa=view;id=1274

I personally find this more interesting than a purely smooth gradient. In this image, iterations were multiplied by 0.01804680000000000173 to get the colour palette index.

[Nahee_Enterprises]

1) Only images of the Mandelbrot Set are allowed.
3) The only post processing allowed is anti-aliasing/sub sampling.

One other thing I'd like to see is a short blurb about
how/why this particular image was chosen.

I too like this idea!!!

But are there limitations as to the rotation of the slice being presented??  And, by post-processing, does that also mean no "layers" being merged together, just a single slice of the M-Set??

And yes, Kerry's suggestion is a good one.

[jwm-art]

No layering allowed either! No rotation!

Hang on.... I'm starting to see a pattern here... All the things that are not allowed are all things the program I've written can't do! But seriously, my basic idea is...

Another thing, an alternative title was "The Imaginary Mandelbrot Competition", or if I'm feeling really indecisive, "The Real Imaginary Mandelbrot Competition".

My basic idea I guess evolved from... The limitations of my programming and maths skills... Well that's not quite true, I've implemented different fractal types, colouring methods, and auto-layering, but... I have this crackpot idea that if I only zoom in deep enough, and make the right choices, there is something in there, waiting to be discovered! So having all these strict rules (I'm mainly trying to work this out for myself here) about what cannot be presented is to place the emphasis on the (creative) possibilities in the set itself, on exploration, on insights, etc, etc.

[LesPaul]

The colour bands may not be replaced by a smooth gradient. This defeats the purpose of exploration and deep zooming. If you want a smooth gradient you only need zoom deep enough.

Well, the normalized color gradients are actually more "correct," if there is such a thing.  The bands are just artifacts (computation errors, in other words) that show up because of the choice made to "bail out" at some hard limit.  People have become accustomed to them because pretty much 100% of the old fractal programs had them.  The Mandelbrot set itself doesn't have distinct bands.  But whatever, if you prefer more of a "retro" contest, that's cool!   

[jwm-art]

Well, the normalized color gradients are actually more "correct," if there is such a thing.  The bands are just artifacts (computation errors, in other words) that show up because of the choice made to "bail out" at some hard limit.  People have become accustomed to them because pretty much 100% of the old fractal programs had them.  The Mandelbrot set itself doesn't have distinct bands.  But whatever, if you prefer more of a "retro" contest, that's cool!  

Oh I see! Hmm. Maybe if I can find information on how that smooth colour gradients are rendered and can implement it, the rules might change ;-)

I was just looking in the programming section at http://www.fractalforums.com/programming/antialiasing-fractals-how-best-to-do-it/ which lead me to HPDZ.NET and the smooth gradients don't look that noticeably different at that level.

Getting OT here, if I do attempt to implement the normalized smooth colour gradient, I hope/expect that it should be able to be stretched out in the same way as I was talking about with the colour bands.

Furtherly OT, I'm still working on the multi-threaded version of mdz Mandelbrot Deep Zoom, it's working but anti-aliasing is borked, and just to get it working I did not bother using the colour palette and it just converts the iterations/colour bands to b&w values. Just got to try and figure out how to put it all back together again.

[jwm-art]

Here's another image to get things started:



( A screen shot because image saving is mysteriously broken in my multi-threaded experiment with mdz, as is anti-aliasing (or more accurately super-sampling) )

Code:

mdz fractal settings
settings
fractal mandelbrot
depth 15000
aspect 1.16666666666666674068
colour-scale 1.00000000000000000000
colour-interpolate no
mpfr yes
precision 80
xmin -1.7685298494202304553484320
xmax -1.7685298494202304553425524
ymax 5.4307321953593614837719382e-4
palette
data
 61 39 11
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[matsoljare]

When i saw the name i thought it would be a competition for images computed using real numbers only.... now that would be a good challenge.

[Timeroot]

Here's another image to get things started:
<Quoted Image Removed>

Huh, I probably sound like complete noob saying this, but I had no idea things like this lurked in the M-set. I really don't have any knack for good fractal exploring. 

[Nahee_Enterprises]

Huh, I probably sound like complete noob saying this, but I had no idea things
like this lurked in the M-set.  I really don't have any knack for good fractal exploring. 

It takes a bit of time to get really good at fractal exploration, learning the many areas and various parameter settings.  And some people have more luck on their side than others.  Either way, it is still a very time-consuming interest/hobby.       

I have spent many hours, days, months, years, and still have much to learn and explore.

[lkmitch]

Here's one.  I've included the Ultra Fractal parameters below.  For those who don't speak UF, here are the center point and magnification:
  x = -1.74734877811384949048239826095235961267258435541015
  y = 0.0022865486943484368266400015529741555193263742956452
  magnification = 4.1e39

I found it by starting at the west midget (largest midget on the spike, center at about -1.75).  I zoomed in to the 1/10 disk and found an embedded Julia on the filament leading to the tip of the disk's structure.  Then, I zoomed in several times, alternating between concentrating on tips and centers of embedded Julia sets.  What I like about this image is that it illustrates the irregular path taken by orbits of points taken from this general area.  Normally, we may be used to thinking about period doubling as a route to chaos.  That's reflected in a doubling of the order of the structure surrounding a midget:  2-fold symmetry surrounding 4-fold, surrounding 8-fold, etc., until it all collapses into visual noise around the midget.  Here, we have an 8-fold structure surrounding a 4-fold.  Going into the center of the image, it proceeds:  8, 2, and 4 and probably more back-and-forth before getting into the final period doubling that leads to the midget.

jan15-a {
fractal:
  title="jan15-a" width=3000 height=3000 layers=1
  credits="Kerry Mitchell;1/15/2010"
layer:
  caption="Background" opacity=100
mapping:
  center=-1.74734877811384949048239826095235961267258435541015/0.00228\
  65486943484368266400015529741555193263742956452 magn=4.1e39
formula:
  maxiter=10000 percheck=off filename="Standard.ufm"
  entry="Mandelbrot" p_start=0/0 p_power=2/0 p_bailout=4
inside:
  transfer=none solid=4294901760
outside:
  transfer=linear solid=4294901760
gradient:
  smooth=yes rotation=125 index=125 color=0 index=325 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

[jwm-art]

"The Reason Why We Always See Bums in the Mandelbrot Set" (don't ask)



xmin -1.7491976289657893741942376816272921165326158557715556129946
xmax -1.7491976289657893741942376816272921165326158557113309627591
ymax -4.2530777152440422725855012159249401150953497611785388221839e-7