Re: Diffuse2d.

[dsumpter]

Hi Nelson,

>Diffuse2d does 2nd order by default (it's a compile time switch in
>Diffuse2d.m). What are the values in the entire nine cell
>neighbourhood? Or are you doing your own algorithm entirely?

I have written my own algorithm and in general I also use 2nd order
neighbourhoods. I just used an example of the 1st order because its
easier to follow. The same problems apply in higher orders.

I didn't actually run a program, I just looked at
the Diffuse2d code to see how you'd done the Swarm implementation and
then did a 'dry run' of what I think would occur. I should note that
my implementation has the same problem (or should I say feature) as
the Swarm version. So I'm not in a position to tell you how to do it 
better.

>In general, this sort of code has two sources of potential problems.
>The discrete approximation has some pathological cases - that's an
>algorithmic problem. There's also a potential programming error, in
>particular overflow. Looking at the code in Diffuse2d it looks to me
>like that could be a real problem (at some point we calculate 20 *
>0x7fff), but I think I tested that code pretty well.

I think we are talking about an algorithmic error (or feature!)
since the same thing occurs in my implementation as Swarms. 
I don't think there is a coding error. 

>>2. Has anyone got a reference they can give me discussing heat
>>diffusion in terms of lattices? I'd be very grateful.

>That's a good question - I'm sure the Swarm libraries could be
>improved in this area. I only implemented the particular algorithm
>that's in Diffuse2d because it happens to be what was in the prototype
>Swarm.

Well, I have Teds references (thanks) now and I'll go and ask one of 
our Numerical Analysists sometime and try and see what the 
alternatives are. I'll keep you posted.....

David.