Very interesting! Tim Hutton has recently investigated similar reaction- diffusion systems; his results are here: http://code.google.com/p/reaction-diffusion/ There are many intermediate things between cellular automata and PDE systems, depending on whether space, time, and states are discrete or continuous. There are a theoretical maximum of eight categories: (0) discrete space, discrete time, discrete states; (1) discrete space, discrete time, continuous states; (2) discrete space, continuous time, discrete states; (3) discrete space, continuous time, continuous states; (4) continuous space, discrete time, discrete states; (5) continuous space, discrete time, continuous states; (6) continuous space, continuous time, discrete states; (7) continuous space, continuous time, continuous states; However, after a little thought, it becomes clear that all automata in (2) are dysfunctional. Some of the remaining systems have already been investigated: (0) Cellular automata (1) Continuous automata (3) Quantum-dot cellular automata (4) Euclidean automata (7) PDE systems I know of no examples in (5) or (6). Sincerely, Adam P. Goucher ----- Original Message ----- From: "Robert Munafo" <mrob27@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, December 24, 2010 6:28 PM Subject: [math-fun] Life-like systems that are continuous and real-valued
Fans of Conway's Game of Life may appreciate this system, which has similar characteristics but has a continuously variable state at each point in a continuous domain (vs. cellular automata, which are discrete in both aspects). Here are some patterns:
mrob.com/pub/comp/xmorphia/catalog.html
and relevant videos:
youtube.com/watch?v=IBrPnp3025I youtube.com/watch?v=-k98XOu7pC8 youtube.com/watch?v=ypYFUGiR51c
The system includes still-lifes, spaceships, rotaters (the nearest equivalent to oscillators), chaotic patterns and a bunch of other stuff. It is a common reaction-diffusion model but with very specific parameter values. More here:
mrob.com/pub/comp/xmorphia/uskate-world.html
-- Robert Munafo -- mrob.com Follow me at: mrob27.wordpress.com - twitter.com/mrob_27 - youtube.com/user/mrob143 - rilybot.blogspot.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun