This is a basic rendering just connecting cells if they are in the same state. It turned out kinda neat. I started with a ball and stick model, but the balls just added visual noise. I think I’ll try rotating a shaded ball next, but the transitions require comparing two models instead of just blending the two images.  
Archives for September 2012
More animated Circles
This page is just playing around with linear paths through the circle space. Â I’ve tried some more complicated shapes but they quickly get too complicated.
A line passing from the bottom of the sphere to the top point of the sphere.
Related Images:
A Pencil of Circles
This is what I was aiming for with the post from the other day.
It’s interesting, but doesn’t have quite the same punch as the “error” version.
Related Images:
Happy Accident #2
I had an error with the length function, but I really like the results.
Related Images:
Circle Test
Generating circles with a mapping from 3 space to the 1 sphere down to the plane.
Related Images:
A Random Walk Through Some Cellular Automatons
I wanted to investigate how closely various cellular automatons that differed by only one term were to each other, so I whipped up a demo that does a random walk through the parameter space of 1-d 2 bit automatons using a neighborhood of 5 pixels. Â This is the first one that popped up.
The next one is a automaton that differed by one parameter and is either off by one either above or below the example above.
As you can see the result is much more regular and I would have considered it completely different, not a close neighbor of the previous rendering. Â Another step:
This is more interesting, but is another close neighbor of previous two.
I decided to start over and in a little more controlled environment, I came up with these two.
And one of it’s neighbors.
As you can see, this part of the space has more closely related images. Â It appears to be close to what I would have expected. Â The more “binary” you get with the 2 value spaces and smaller neighborhoods the less related the images are, and the larger the pixel and neighborhood spaces the more “continuous” the behavior becomes. Â That doesn’t mean that the hard boundaries go away, and I’m sure many measures of the resulting spaces have a self similar structure, which would be interesting to investigate in and of itself.
My next plans involve, showing single pixel deviations in the initial state, and then building graphs of all the positions of the automaton spaces. Â I’d like to compare how the graphs change as you make the automaton space larger. Â I still have more predator prey stuff on the back burner too.
Related Images:
Cellular automaton #1
Well, it’s time to switch gears again for a little bit. Â I finally threw some simple code together for a 1d cellular automaton, and the patterns are fascinating. Â I’ve got a few ideas to work through with these. Â I’m not sure if there is anything worthwhile in this vein, but I see how fascinating they are now.
Related Images:
Parameterized Prey Peaks
This is a very rough render of the first 25 peaks as the focus point of the predator prey equation is rotated in a circle at a varying frequency. Â I need to do better peak estimation to pull out some of the jaggedness, but it’s already a more interesting pattern than the logistic equation.
Related Images:
Disintegration
The tighter you hold on, the more things fly apart.