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Hi!

I always wanted to have a nice reference picture that contains all colors.

The first idea that comes to mind is slicing the rgb cube and tiling the squares together. One example looks like this:


4096x4096: http://dl.dropbox.com/u/11704339/testbilder/rgb_standard.png

But it is pretty boring and does not look like it contains every color to the eye. It seems to me like yellow and gray is missing.
Compare it to this:



This does not contain every color and I did not create it. But it looks much more colorful to me.

Now my idea was, to arrange all colors on a line:
Start with rgb=0x000000 and increase it up to rgb=0xFFFFFF.
Now arrange that line on a level 12 Hilbert curve.



The result looks like this:


4096x4096: http://dl.dropbox.com/u/11704339/testbilder/rgb_hilbert.png

Much more interesting. But still, it looks like it is made of even less colors than the first pic.

And now sit down and grab on to something:
I went through the rgb cube on a 3D Hilbert curve...



and arranged it on a 2D Hilbert curve.
The result looks like this:


4096x4096: http://dl.dropbox.com/u/11704339/testbilder/rgb_superhilbert.png

I think, this looks very interesting and colorful.

And what did I find while I was googling for some Hilbert curve pix to show in this post? It has been done before. Of course.
http://corte.si/posts/code/hilbert/portrait/index.html
http://allrgb.com/hilbert-curve

Still, I think creating a picture that contains all colors (once) and also looks like it contains all colors is a nice challange.
The clou would be to find a picture that is smooth without hard transitions.

I hope I encouraged some people to post their ideas

EDIT: Sometimes life sucks. http://allrgb.com/

Cheers!

Mircode: Don't despair that you were preceded by two other people, the internet does that. There's a lot of bright minds freely sharing their ideas. One of the two pre-discoverers is a Google company employee. To parallel discover this, you have impressive "company", so to speak.

It looks like the image needs a few orientations to maximize similarity between edges of the squares. Also, another idea comes to mind is self organizing maps where similar pixels group together on the 2D image.

-mike

Hihi, no need to cheer me up I am not really moping.

To msltoe:
I will try some reorientations. I think 24 different are possible in general but some of them should look equal due to symmetry. And what could be even more interesting: Rotating not only by 90° but also different angles and still getting all colors with some modulo operations (except there will be rounding errors so some colors will be there twice and some will miss).

EDIT: 48 should be possible. In contrast to a real dice, a theoretical one can be flipped

To cKleinhuis:
One color channel has 2^8 colors. So with three channels there are (2^8)^3=2^24 colors. The nth iteration of the 2D Hilbert curve covers (2^n)^2 points, for 3D (2^n)^3. So for 2D n has to be 12 and for 3D it has to be 8. This results in a 4096x4096px image.

any way that guy also has an idea to use hilbert-ordered colors for sorting viz, but what if we use it as a palette for classic stuff like mandelbrot? who did that, or who will be 1st to try?

I made a new picture. Same idea as the Hilbert thing, just another curve.

For the 2D path I took the H-order curve which I found here:
http://www.win.tue.nl/~hermanh/stack/dagstuhl08-talk.pdf

it looks like this:


And for the rgb cube I tried to recreate the principle of the curve in three dimensions, which looks like this:


Aaaand the result:

Mircode,
This curve works better. The "mural" could easily be considered modern art. There is a Gestalt mixture of diamonds, triangles, squares.
There are methods for optimizing the position of colors to minimize the distance between neighbors, but this is more aesthetically pleasing.
-mike

Color contains all the information. Pixels are just building blocks.

What fascinates me about fractals is that when certain formulas and narrow parameters are  selected information is created out of chaos or "empty" ground state.  For example when you zoom out enough out of the mandelbrot set then there is just void.

Mandelbrot set is not chaotic structure. It is highly deterministic but also highly unpredictable. It seems to get more interesting and complicated when you zoom deeper and deeper (and also when the program becomes annoyingly slower and slower no matter how fast computer you have got).