User talk:Sam Derbyshire

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[edit] Lambert W function, graphs, ...

Hi Sam

Love the Lambert W function pictures! Do you mind if I clarify that the surfaces are the principal branch?

Best wishes

Robinh 19:44, 25 November 2006 (UTC)

Hi,

Well I thought it was clear it is the principal branch (as I wrote W₀) but of course, go on and add that, I don't mind (why should I ? :D)

Thanks,

(I'm thinking about doing the same for logarithm and exponential, should I ?)

--Xedi 19:53, 25 November 2006 (UTC)

Hi again Xedi . It did say W₀. I missed that! Check out Weierstrass elliptic function for another visualization scheme for complex functions.

Best wishes, Robinh 21:35, 25 November 2006 (UTC)

[edit] Nice graphs.

Your graphs of those functions are truly awesome - I'm just having a crack at something like it with MuPADs free trial, but I can't get the projected contour lines and the contours lines on the plot itself to work properly. Perhaps it's because I'm not used to the Maple-esque environment - I generally use Mathematica for most "serious" work, but since the object here is to make it look as good as possible as well, I'm branching out. However, MuPAD's fighting back with spirit!

For a start, I'd quite like to redo some quantum wavefunction graphs on Commons, and I'd like to see if I could make them look half as good as yours.

Also, how do you get the images to be all oriented the same way? I can never get them back the way they were after making them bigger or whatever...

Sorry to be such a pain, but I would love to know how to draw graphs like that.

inductiveload - on Commons - that's where I'm most active.Inductiveload 20:18, 13 February 2007 (UTC)

Sorry I had written a reply in the edit box thing and I had left it while i tried to plot sometihng to see it it was worth mentioning, but my PC crashed (I used all my RAM on Mathematica and muPad combined....I was even watching the CPU usage at the time). I thought I had saved my post but clearly not. I was quite busy picking up the pieces! It's time like that I wish I used Mozilla which doesn't lose form data like that...

I've spent several hours now wresling with MuPAD, and I'm begiinging to get results! How do you stop the contour lines (the projected ones at the bottom) from getting all chopped up? Inceasing the SubMesh seems to make the gaps smaller (so they get lost in the resolution), but there are more of them if you zoom in. The only thing I can think of it plottong each one ith it's equation, but I'll be damned if i'm going to do that!

I've figuredo ut the camera position control, so all my graphs are from the same angle which is good...

Also the colouring's a little tricky - I have a sort of hacked-together function doing it ATM (complete with trial-and-error values), which works OK but goes a bit monochomatically pink in the middle).

colourfunc := zip(RGB::Red, RGB::CornflowerBlue,
                 (a, b) -> (f(x,y)+6)/(12)*a
                          -(f(x,y)-6)/(20)*b):

I haven't had a chance to see if it looks better in orange and yellow or some other combo.

I'll polish up one of my plots and post it on Commons in a bit. Then I might have a go at a Taylor series or something - that seems to lend itself well to this.

Thanks again,

Inductiveload 19:00, 16 February 2007 (UTC)

For the contour lines at the bottom, If you're talking about what I think, just put their opacity down (quite funnily, at opacity=99% (or whatever except 100%), the choppiness disappears)).

For the colouring, actually, I mostly use the simple dichromatic way, not a custom function for the colour. But, after seeing for example the klein surface in your gallery, I really see the benefits of not simply doing a z-based colouring. I've tried to come up with some colouring functions, but well, they aren't great. Actually I spent a lot of time trying to get nice "density" plots (like your black and white plots of wavefunctions) in colours, but had a hard time antialiasing the borders (to be like these http://mathworld.wolfram.com/images/eps-gif/ParabolicCylinderDContours_851.gif), I finally ended up doing a geometric mean that smoothes the borders...

I'll try to find a better way for colouring graphics, especially a way to get something resembling the Mathematica colouring I quite like on some plots (like your Klein surface plot),.

About Taylor series, maybe you've noticed the few plots I did on Wikipedia, I personnally quite like the animation of the approximation of cos(x) over the complex numbers with Taylor Series. I've also used the equation you gave for the Fourier Series for a periodic x^3 function to do an animation.

One thing that I really like with MuPad, is the quality of the help inside it : I've learnt about everything just looking up in the help.

If you would like more advice, please say so, I'm happy to help. --Xedi 19:47, 16 February 2007 (UTC)

The Mathematica plots are coloured by having lots of differnet coloured lights shining on them from differnet angles, I think. I'll check for you. I have to catch a train now, I'll post back tomorrow proabably with details.

The tip about the opacity was right on - thanks a lot. I can't find a way to put subscripts or special characters (like ψ) in the axes titles, though - do you know how to do that? I'd be interested to see the Fourier series animation - is it a complex one or a real one? I can see how that would shape up nicely - I might try it on the train.

I agree, the help uis good on MuPad, it's just learnig a whole new package with its quirks (eg. sin(x), not Sin[x]) take time. if you ever use Mathematica, check out this site for some really good antialising code. Be warned though - it will kill your computer for the time it's working!

Inductiveload 20:35, 16 February 2007 (UTC)

Hi there - I've found out about Mathematica's lighting:

The default lighting used by Mathematica involves three point light sources, and no ambient component. The light sources are colored respectively red, green and blue, and are placed at a angles on the right‐hand side of the object. Objects are by default coloured matte white.

It shouldn't be too hard to replicate this in MuPad. I haven't tried yet, though. I have also uploaded a Wavefunction plot here

Inductiveload] 16:54, 18 February 2007 (UTC)

Thanks !

But I don't seem to be able to correctly replicate that lighting as MuPad lighting gives reflections... I tried to change the lighting to flat but it only gets worse...

Oh well, don't hesitate to say if you find out how to do !

Thanks again, --Xedi 16:59, 18 February 2007 (UTC)

MuPAD seems to have quite a shiny surface -Mathematica uses a purely matte (reflects light in all direcetions, like a sheet of plain paper) white surface. I'm not sure how to change this in MuPAD. Perhaps you old use DistantLight to simulate it (it's more like sunlight). The help page on this shows some exmaples.

129.31.77.98 22:47, 18 February 2007 (UTC)

Yes, sadly I can't see any options to make the surface matte. Oh well, I guess a color function could be made to give the same results, but I suppose it will need a lot of fine tuning...

--Xedi 23:55, 18 February 2007 (UTC)