http://texturegarden.com/java/rd/

Some seriously interesting stuff happening in there. Now if I could just 
figure out the equations involved...

(One day I really must learn how to comprehend differential equations!)

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> http://texturegarden.com/java/rd/
>
> Some seriously interesting stuff happening in there. Now if I could just 
> figure out the equations involved...

I thought you were trying to simulate an organ pipe.  Still, I think you'd 
have more chance making one from wood than getting a simulator working that 
produces a recognisable organ sound :-)

> (One day I really must learn how to comprehend differential equations!)

What bit don't you understand about the reaction/diffusion equations? 
There's nothing in there different to the wave equation.

In each cell, U and V are the amount of each chemical.

dU/dt = Du * L(U) - U*V^2 + F*(1 - U)
dV/dt = Dv * L(V) + U*V^2 - (F + k)*V

Du, Dv, k and F are constants.  L(x) is the Laplacian operator, which you 
know from the wave equation (2nd differential in each direction added 
together).

So just calculate the right side of those equations, and that will tell you 
how much U and V should change.

Seems simple enough to me to implement if you've done the wave equation.

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scott wrote:

> I thought you were trying to simulate an organ pipe.

You know me - if there's a way to use mathematics to produce trippy 
visuals, it must be done! ;-)

> Still, I think 
> you'd have more chance making one from wood than getting a simulator 
> working that produces a recognisable organ sound :-)

Well, I suspect I'm doomed to fail either way, but hey! :-P

>> (One day I really must learn how to comprehend differential equations!)
> 
> What bit don't you understand about the reaction/diffusion equations? 
> There's nothing in there different to the wave equation.
> 
> In each cell, U and V are the amount of each chemical.
> 
> dU/dt = Du * L(U) - U*V^2 + F*(1 - U)
> dV/dt = Dv * L(V) + U*V^2 - (F + k)*V
> 
> Du, Dv, k and F are constants.  L(x) is the Laplacian operator, which 
> you know from the wave equation (2nd differential in each direction 
> added together).
> 
> So just calculate the right side of those equations, and that will tell 
> you how much U and V should change.
> 
> Seems simple enough to me to implement if you've done the wave equation.

The hard part is FINDING THIS EQUATION! >_<

I've found several sites about this stuff, but none of them present a 
formula I can comprehend. Now that I have a working formula and I know 
what all the variables are supposed to be, I stand a chance...

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> The hard part is FINDING THIS EQUATION! >_<
>
> I've found several sites about this stuff, but none of them present a 
> formula I can comprehend. Now that I have a working formula and I know 
> what all the variables are supposed to be, I stand a chance...

Wikipedia has a more general form under the "Reaction Diffusion Equation" 
page, the U*V^2 + F... bits on the right side are specific, and the ones I 
posted are from the "Grey-Scott model".  I only know that because there was 
a chapter in GPU Gems where they implemented it :-)

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scott wrote:

> Wikipedia has a more general form under the "Reaction Diffusion 
> Equation" page, the U*V^2 + F... bits on the right side are specific, 
> and the ones I posted are from the "Grey-Scott model".  I only know that 
> because there was a chapter in GPU Gems where they implemented it :-)

LOL! Yeah, everybody uses the Grey-Scott model, apparently. (Probably 
because it's the only one they can find equations for!)

Now we know what Doc Brown was yelling about all those times he said 
"Grey-Scott!" ;-)

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