Fractal fire and other fractal life

[Tglad]

I had an idea the other day to take Conway's life, or cellular automata like that, and make it fractal by applying the rules to each level of detail.
Here's a video of the results for various mapping tables:

<a href="http://vimeo.com/moogaloop.swf?clip_id=36816056&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=36816056&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

The fires kind of remind me of animations of the sun.
The second fire and the wobbly blob at the end are my favourites.

[asimes]

It looks very cool but I'm uncertain what you mean by applying the rules at every level of detail. I'm familiar with Conway's Game of Life but I have no idea what is going on in the video.

[Tglad]

First, generalise Conway's game of life by saying that the bit state of the centre pixel is any function of the 3x3 pixels in its neighbourhood.
Second, replace the 2d grid with a hierarchy of 2d grids, each higher level has a quarter as many squares, twice the size.
Third, for each cell, include the four nearest neighbours on the level above and the level below in your neighbourhood. So the new value of each bit is b = f(2x2 parent bits, 3x3 sibling bits, 2x2 child bits).

Then you iterate this function on all the bits on all the levels and draw the animating result of the highest resolution grid.

The video shows the results for different functions, or different mapping tables. Some look like fire, some like froth etc. I wrote the program and found these different effects by varying f() randomly, picking nice looking results and repeating.

They are probably dynamic fractals, like discussed here: http://www.fractalforums.com/ifs-iterated-function-systems/fractally-animating-fractals/  rather than just a fractal moving smoothly.

[hobold]

Some of those automata seem to have just the right amount of foamy boiling/bubbling that is needed to look good when viewed as a 3D volume of slices rather than a time series of 2D images.

[s31415]

Interesting...

It reminded of a very cool fractalish property of Conway's game of life: it can simulate itself! Check this video:
http://www.youtube.com/embed/QtJ77qsLrpw
Details here:
http://www.conwaylife.com/wiki/OTCA_metapixel

[Tglad]

Yeah that is pretty clever.
If you want to find your own fractal automata then here is the .exe that I wrote, plus examples that you can load:
https://docs.google.com/open?id=0B8S7Si-yu3DoOGJhNDVmZDctZDIyYy00NWFmLTg3OGEtOWVmNGU3OTMyZmNm

And here's another little one, it reminds me of an amoeba:
<a href="http://vimeo.com/moogaloop.swf?clip_id=36867848&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=36867848&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

[Tglad]

And here are two more petri dish specimens:

<a href="http://vimeo.com/moogaloop.swf?clip_id=36951270&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=36951270&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

If you like them you can make your own by downloading the tool mentioned in the last post.

[Tglad]

I have updated the tool, and it is presented here: https://sites.google.com/site/tomloweprojects/scale-symmetry/automataFinder
The sixth type generates traditional fractals, for those who don't like going near the dynamic kind.

[Tglad]

Some images for static fractals generated with a new rule (type 7):








The executable is updated on the site.

[kram1032]

That last one lacks an image or a video to be seen.
Though, this stuff looks neat

The link above doesn't work either :-/
It should be:
https://sites.google.com/site/tomloweprojects/scale-symmetry/automataFinder
But I can't download the file since it just opens a browser to few the files inside individually...

I'm almost certain that, given enough fiddling around, you find small reproducable elements that just work out...
I guess, some clever wavelet-analysis could establish connections between the two...
What I could do is downloading each file individually, but that's kind of annoying...

Edit: Ok, I bypassed the viewer by using itself xD...



That's a fractal type 7
I tried to look athe the page that's linked to above and it opens the htm document...
Since I already was there, I just searched for the link of the zip and behold:
https://sites.google.com/site/tomloweprojects/scale-symmetry/automataFinder/FractalAutomata.zip
It works...

Edit2:
Are the mutations you do genetic or entirely random?
Maybe you could somehow keep track of most liked changes to basically make it "evolve" towards the most interesting outcomes...
You could even try something like making the six options compete with each other, each trying its own tactic to get clicked on... That way, it might be possible to slowly but surely get to THE structure you want...

More type 7

I'd love to see a house that uses such a layout...

[Tglad]

Hi Kram, thanks for correcting me, yes that is the URL. To download the zip, click the little downwards pointing button on the right at the bottom of the page. I have also fixed up the images in my last post.

The mutations are random. The rules for each one are a list of bits, and I mutate by flipping a few percent of the bits at random.

"Maybe you could somehow keep track of most liked changes to basically make it "evolve" towards the most interesting outcomes.."
Yes, that might work. I guess the challenge is how to make more interesting shapes available while avoiding results that just look like white noise. The different types do it to different degrees.

"You could even try something like making the six options compete with each other, each trying its own tactic to get clicked on... That way, it might be possible to slowly but surely get to THE structure you want."
I like this idea Kram, like the shapes get rewarded if they are clicked on. If I made the app online then every click by a user could be sent back to the server and make that shape more likely to show up. Though I don't think I can get the app fast enough on a browser, even with webGL.

As it stands you are the only one apart from me who has ever tried this out, so thanks for giving it a go! and notice that you can load the different example files.

[Alef]

I think it would require an additional colour dimension. Say it have nice patterns, but bichrome so not much seen in insides.

[kram1032]

Yeah, changing the color that's used or even doing something like per-detail-layer colors could lead to interesting results.
For instance, assign the different layers different wavelengths and add them together for a full image
There are surely plenty of ways to get nice coloring going...

[Tglad]

Nice idea.. hopefully I'll get colour in eventually.
Here's a couple more from type 7-

[asimes]

Admittedly I have never tried to make a fractal Conway's Game of Life, just 2D grid variations (Hexagon, Triangle, ext) and a 3D version. However, for any of these grids interesting colors can be made by neighbor counting rules. For example, one color could be influenced only by neighbors up, down, left, or right... another by the diagonals... another by more distant neighbors... ect.

EDIT: That flowers image is particularly nice. Could you explain what is going on please in that one?