> How did you arrive at
>
> #local XD = waveHeight[X+1][Y] - 2*waveHeight[X][Y] + waveHeight[X-1][Y];
>
> According to my calculations,
>
>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =

That should be a "-" in the middle, because you are taking the differential 
of the differential.

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>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =

Oh, and just for clarity, you should probably write that as:

(v[x+1]-v[x]) - (v[x]-v[x-1])

rather than:

(v[x-1]-v[x]) - (v[x]-v[x+1])

In your case it makes no difference because you are differentiating twice, 
but in general differentials are usually defined to be positive if v[x] 
increases with x.

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>> Chapter 8, "Implications for everyday systems", section title "Fluid 
>> Flow", page 376 in my hardback copy.
> 
> Thank you!

;-)

Well, go implement! :-P

>> It makes some valid points... it's just not very interesting to read.
> 
> I found it pretty interesting, but repetitive. I also really like CAs.

I find CAs to be dull and boring.

>>> I trust you've read Godel-Escher-Bach?
>> Never heard of it.
> 
> http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567
> 
> Wow.  I'm not sure why it came up in the conversation, but it's a 
> must-read for anyone who enjoys computers and waded thru Wolfram's stuff.

I actually didn't bother finishing to read it. It didn't have anything 
much interesting to say.

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>> How did you arrive at
>>
>> #local XD = waveHeight[X+1][Y] - 2*waveHeight[X][Y] + waveHeight[X-1][Y];
>>
>> According to my calculations,
>>
>>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =
> 
> That should be a "-" in the middle, because you are taking the 
> differential of the differential.

The above formula is only meant to be the 1st derivative. I run it twice 
to get the second derivative.

Except that, as noted, my code fails miserably, whereas the formula you 
used seems to work perfectly for some reason...

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Darren New wrote:

> http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567
> 
> Wow.  I'm not sure why it came up in the conversation, but it's a 
> must-read for anyone who enjoys computers and waded thru Wolfram's stuff.

If it's your thing, I must recommend:

http://www.amazon.co.uk/Linked-Everything-Connected-Business-Everyday/dp/0452284392

It's a really nice book. (E.g., did you know that the software marked is 
like a Bose-Einstine condensate? If you care about such things, you'll 
love this quirky little book...)

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>>>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =
>>
>> That should be a "-" in the middle, because you are taking the 
>> differential of the differential.
>
> The above formula is only meant to be the 1st derivative. I run it twice 
> to get the second derivative.

To get the 1st derivative you just need:

v[x+1] - v[x]

What you are doing is to essentially average the differential of one point 
and the point before, which is going to blur out any sharp gradients.  (eg 
if you have points 5 0 5 the gradient your way will come out as zero)

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Invisible wrote:

> 
>> Thinking of writing a simulator? ;-)
> 
> Well let's put it this way: What do you think my chances of building a 
> working set of organ pipes are? :-P Last time I tried to cut wood, I 
> couldn't even cut it straight! :-/ I figure I have far more chance of 
> building an organ simulator...

Reminds me of something I had some time ago. It was a software synth 
based on the physical characteristics of the instrument, I think it was 
put out by Creative at the time, bundled with their sound card. I've 
since forgotten the name of it, though. Ahh, called WaveGuide:

http://en.wikipedia.org/wiki/Digital_waveguide_synthesis

Interesting technology. Good luck if you do produce a pipe organ simulator.



-- 
~Mike

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Mike Raiford wrote:

> Reminds me of something I had some time ago. It was a software synth 
> based on the physical characteristics of the instrument, I think it was 
> put out by Creative at the time, bundled with their sound card. I've 
> since forgotten the name of it, though. Ahh, called WaveGuide:
> 
> http://en.wikipedia.org/wiki/Digital_waveguide_synthesis
> 
> Interesting technology. Good luck if you do produce a pipe organ simulator.

The Reaktor product from Native Instruments features a sound module 
named "Steam Pipe" which uses a (1D) digital waveguide to simulate 
string and wind instruments. It does a delightful flute sound. ;-)

(What can I say? I like flutes!)

It's really interesting. You can "over-blow" the flute just like a real 
one. It sounds ever so believable.

Of course, Steam Pipe does all this using a few non-physical shortcuts. 
(E.g., instead of a true gas turbulence engine, it uses a simple 
nonlinear waveshaper to produce wave saturation.) The next step would be 
to move to 2D or even 3D with real turbulence simulation. I suspect this 
would result in an instrument that takes weeks to simulate and doesn't 
sound all that much different.

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Invisible wrote:
> I actually didn't bother finishing to read it. It didn't have anything 
> much interesting to say.

Wow. OK.  I'll note that it took me several readings to even realize it 
was two books in one cover, for example, in spite of the author telling 
you so several times.  It's a rather complex tome.  But if it's not your 
thing, I can understand that... :-)

 > http://www.amazon.co.uk/Linked- ...

I'll check it out, thanks!

-- 
Darren New / San Diego, CA, USA (PST)

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Invisible wrote:

> Of course, Steam Pipe does all this using a few non-physical shortcuts. 
> (E.g., instead of a true gas turbulence engine, it uses a simple 
> nonlinear waveshaper to produce wave saturation.) The next step would be 
> to move to 2D or even 3D with real turbulence simulation. I suspect this 
> would result in an instrument that takes weeks to simulate and doesn't 
> sound all that much different.

To do things in realtime, you must take shortcuts :)

Wonder if there's a sound card out there that has a programmable DSP 
that's got enough parallelism to add as much realism to your simulation 
as possible.
-- 
~Mike

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