POV-Ray : Newsgroups : povray.off-topic : Differential equations FTW! : Re: Differential equations FTW! Server Time
11 Oct 2024 01:22:12 EDT (-0400)
  Re: Differential equations FTW!  
From: Paul Fuller
Date: 8 Jan 2008 09:54:31
Message: <47838ea7@news.povray.org>
Invisible wrote:
> Mmm, apparently I'm the only person retarded enough to actually be 
> amused by these.
Not at all.

> 
> Then again, when I was a child, I used to sit for hours watching the 
> washing machine. [Remember that when I was a child, "TV" was only 
> available for a few hours a day...]
> 
> Does anybody know how either of these simulations actually work?
> 

Cellula Automata - Each cell (pixel) follows some simple rules based on 
its current state and that of its neighbours to determine its state in 
the next generation.

This particular example looks like it implements some equations that 
model the reaction of chemicals in 2D.  There are real mixtures that 
exhibit the pulsating and alternating patterns that some settings reproduce.

Fiddling around with the parameters gives some behaviours that are 
interesting and some that quickly lead to all dead, all alive or 
something else.

The number of possible combinations of the parameters is huge but there 
are typically a small number of interesting classes of behaviour on the 
boundaries between boring and chaotic.

Some behaviours strike us as biological which I think sheds light on how 
  complex life can emerge from simple chemical and physical rules.

You probably know already that this is known as 'emergent behaviour' - 
When a system exhibits some behaviour often at a large scale that you 
can't really predict from the rules.

I found a couple of nice settings.  Not sure if anything similar is in 
their presets:

			Bees	Spaceships
Rate (Agent)		1500	982
Rate (Inhibitor)	6190	12853
Speed (Agent)		230	50
Speed (Inhibitor)	85	41
Scale (Agent)		15	15
Scale (Inhibitor)	15	14

For 'Bees' start a small pattern in the middle.  One or more individuals 
proliferate by binary division and quickly fill the available space. 
Then they start to pulsate in some not quite discernible way. 
Occasionally an individual dies but the surrounding cells quickly split 
and fill the available space to repair the colony.

'Spaceships' is like the similarly named constructs in Conway's Life.  A 
bit larger and you can imagine a plasma drive towards the rear.  Start 
with a bit more random stuff and you get lots of spaceships cruising 
around.  Occasionally they meet and one or both are destroyed.  Some 
'self-repair' after close encounters.  Interesting thing is to vary the 
Speed (Inhibitor) around 41.  Take it down and the ships reduce in size. 
  At 37 they suffer spontaneous explosions after a time and are all 
destroyed.  From around 43 upwards the trailing edges continually break 
off to form new ships and it becomes too chaotic.

Fun stuff.  Thanks for the link.


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