User talk:LucasVB

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Should you be forever blessed for the awesome animations you make![edit]


Hello! I'm curious: which software did you use to generate the animation illustrating matrix transposition so beautifully?

Check the FAQLucasVB | LucasVBWikipedia | Talk 12:51, 12 April 2013 (UTC)


Bem vindo ao Commons:Featured picture candidates e parabéns pela sua animação (se vai ou não ser promovida a FP é outra história...). Precisamos de gente como você e de mais animações com conteúdo técnico e científico. Eu próprio tenho tentado fazer algumas pequenas coisas (craveira, sextante, quadrado desaparecido), mas sinto-me muito sozinho e não tenho nem suas ferramentas nem o seu talento. Convido-o a participar mais activamente naquele fórum, apresentando os seus trabalhos e contribuindo com a suas opiniões para melhorar o dos outros. Entretanto, que tal começar por nomear um dos seus giroscópios? - Alvesgaspar 22:52, 21 January 2007 (UTC)

Opa, obrigado! :) Eu venho contribuindo com animações e imagens técnicas ou científicas já faz um tempo, e pretendo continuar contribuindo. Agora, por mais que eu goste de minhas imagens e animações (especialmente a do giroscópio e a dos circulos de Villarceau, que é FP na Wikipedia em inglês), eu não me sinto impelido em me auto-nomear à FP. Acho que se as imagens forem realmente de boa qualidade, elas serão eventualmente reconhecidas por mérito próprio entre a comunidade. Sinta-se livre para nomeá-las, se você realmente acha que elas merecem o status de FP... Agora, eu não costumo me envolver muito com a comunidade Commons. Geralmente eu invisto meu tempo e atenção na Wikipedia em inglês mesmo. — Kieff | KieffWikipedia | Talk 23:39, 21 January 2007 (UTC)


Hi, could you please have a look at Image talk:Exponential.png? Melchoir 23:32, 5 March 2007 (UTC)


Hey, I saw this file you uploaded and liked it - Image:Hyperbolic triangle.svg. Would you be willing to make a similar image to describe en:Elliptic geometry? This page has no graphics whatsoever, and something like that is very helpful to picture the concept. Thanks - Sarregouset 20:55, 5 September 2007 (UTC)

Flaw in Image:Light dispersion conceptual waves.gif[edit]

Light dispersion conceptual waves.gif

Hi. I should have dropped a note to you about this before: Image:Light dispersion conceptual waves.gif has a serious flaw. The red waves are clearly moving faster than the violet waves outside the prism, which is unphysical (neglecting the dispersion of air. This image should not be used as-is. --Srleffler 00:09, 17 February 2008 (UTC)

Crap, you're right! I did have that coded, but apparently it didn't run. I'll get it fixed as soon as I find some time. Sorry. 00:15, 17 February 2008 (UTC)

Periodic functions in WZGrapher[edit]

Hello Kieff!

I have one simple question: how do you plot i.e. a sawtooth-wave function in WZGrapher? I saw your image called Periodic_identity and I would like to know how to achieve that.

Best regards,


April 11, 2008

Light dispersion image[edit]

The latest version of File:Light dispersion conceptual waves.gif looks better aesthetically, but has problems displaying in thumbnail form: An error message is generated saying: "Error creating thumbnail: Invalid thumbnail parameters or PNG file with more than 12.5 million pixels" I am going to revert it to your previous image which still works. ~ Kalki (talk) 17:06, 6 April 2010 (UTC)

Oh well — I tried that, and that didn't work either — there seems to be some glitch in the current software preventing a proper display of the image in thumbnail, even when I reverted it to the previous version — I reverted it back to your latest, but the problem remains. ~ Kalki (talk) 17:11, 6 April 2010 (UTC)

Sources for your POVray images[edit]

Hi, could you please upload sources with your POVray images? It will make them easier to modify and adapt. Especially, I'm interested in the sources for this image — I'm going to create illustration for the article ru:Граф Риба based on it.


Ilya Voyager (talk) 08:20, 13 June 2010 (UTC)


Hi, I enjoyed your animation on the singular value decomposition featured on Wikipedia. However, if possible I would suggest to change the Sigma matrix entries from what is currently shown (Sigma_11, Sigma_12, Sigma_21, Sigma_22) to (sigma_1, 0, 0, sigma_2) to reflect the diagonality of that matrix and the connection to the illustrated singular values. Cheers, Philip

Hi, I don't understand your change [1] in description of File:Singular-Value-Decomposition.svg. I chose the unit vectors as in x-direction (pink and horizontal right) resp. in y-direction (yellow and vertical up). Obviously M sends to and to which is true for the original version but false after your change. --Georg-Johann (talk) 20:04, 16 September 2010 (UTC)

Well, when I used that matrix for the animation based on that image, it didn't match the transformation depicted. So I thought it was just an error you did when inputting the matrix. I see now that I just accidentally flipped things in my code: I used a row matrix instead of a column matrix for the coordinates. My bad. — Kieff | KieffWikipedia | Talk 20:29, 16 September 2010 (UTC)

Thanks. I saw the animation and was wondering why the basic transformations get further decomposed into mappings that do no more have the properties of svd components?

For example orthogonal U is decomposed into two shearings again (whereas the svd decomposes the shearing into a orthogonal-scaling-orthogonal sequence). The decompositions of U are no more orthogonal so that the indicators for σ are no more orthogonal in the intermediate frames. The overall animation leads (at least for me) to the impression of 6 transformations rather than 3 and tend to make things more complicated rather than to work out an example as easy as possible (without being trivial).

The intermediate frames could be as follows, which would reduce the number of trafos perceived to 3: 1. V is just a rotation in order to preseve orthogonality:

2. Σ is a scaling that "generates" (the absolute value of) the determinant of M, i.e. the size of the blue area is preserved because det M=1. So intermediate frames would fade in the σs and the trafo would be generated by means of

3. U ditto V

What do you think? --Georg-Johann (talk) 14:13, 17 September 2010 (UTC)

I thought about it, but it seemed to be more interesting to show the effect of each column, as described in the article. In the context of the article, it seemed better to me. It says:
The columns of V form a set of orthonormal "input" or "analysing" basis vector directions for M. These are the eigenvectors of M*M.
The columns of U form a set of orthonormal "output" basis vector directions for M. These are the eigenvectors of MM*.
The diagonal values in matrix Σ are the singular values, which can be thought of as scalar "gain controls" by which each corresponding input is multiplied to give a corresponding output. These are the square roots of the eigenvalues of MM* and M*M that correspond with the same columns in U and V.
That way, you can see the effects of each column of the matrix, and how each represents an orthogonal transform, hence why each column is highlighted individually. If one thinks the entire matrix is acting upon in the intermediate frame, the problem you described would arise, but I didn't think it would be misleading. A quick edit in the description could solve this issue, I think. Or, maybe adding the orthogonal lines in those intermediate transforms, with arrows showing that the intermediate steps are still orthogonal to their original orientation.
Also, from experience, most people don't understand these matrix transforms because they can't see how two shearings can result in a rotation. A straight, full-matrix transform animation that results in a rotation also has the effect of the shape "squeezing" as both shearings are in their intermediate steps, which always looked rather misleading too. This was supposed to help in that respect too.
Either way, I can easily make an animation without the per-column transforms. I'll render it and upload shortly. If you think it's wiser, use that version instead. Cheers! — Kieff | KieffWikipedia | Talk 15:46, 17 September 2010 (UTC)

Rotating point on a sphere-like degenerate torus[edit]


First off, I love your image of a sphere like degenerate torus!

Secondly, I request that you please make a gif of a rotating point on the circle that when rotated about the torus's axis, creates the torus. This rotating point would inscribe a spiral upon the surface of the torus. Add to this the degenerate and regenerate functions of the image, bringing the torus into and out of singularity, and you got it.

I feel this motion represents consciousness and the reality of existence to a very high degree, as it includes the regeneration of singular unity and the degeneration of separate division, all within a cyclical storyline that needs both.

Thank you in advance for the honor of inviting such a request.

All the best, Matthew

What software[edit]

Hi! Some very nice graphics! In your gallery you stated what you used for the 3D images, but what about the rest? What softwares have you been using for the different images? Thanks. -- Ekborg

It depends on the image. this old revision of the page has some detailed information on the old images. The new ones I've made recently all used a PHP toolkit I'm writing called GDCanvas. I hope to release it soon enoug. — Kieff | KieffWikipedia | Talk 15:13, 31 July 2012 (UTC)

Multi-Variable Animation Request[edit]

Hello Lucas,

My colleague and I are building a multi-variable calculus course for gifted high school students, and we were hoping you'd be able to create an animation for us. We absolutely loved your animation for scalar and vector line integrals; they truly captured the fundamental concepts of what's going on behind all the notation.

We're trying to explain the concept of a unit normal vector field (essentially a choice of orientation) on a surface, and how it induces a direction on its boundary. The text book we have chosen for the students does not do a very good job of explaining this concept, so we tried to explain ourselves, in terms of "gears". Below is a portion from our explanation:

Let be an orientable surface with boundary curve , and pick a unit normal vector field on . We say that is traversed -positively if the direction along gives it a right-handed relation to the field near the boundary.
Recall that in a right-handed coordinate system, a counter-clockwise rotation is associated to a normal vector. Then we would say a boundary is traversed -positively if the direction matches up with the counter-clockwise rotation of normal vectors near the boundary. Think of the base of a normal vector as a gear, which is turning counter-clockwise, and think of the boundary as a conveyor belt being moved by the gears near it. The direction the belt travels depends on how the gears near it are turning. Parts of the boundary near the edge the surface, and parts of the boundary around a hole in the surface will be traversed in opposite directions. The image below should help to make this clearer:

The animation we had in mind would go something like this:

  • Opens with a surface embedded in . Something simple, like a warped sheet should be fine. The surface should have a boundary and a "hole".
  • Next, a unit normal vector field appears on the surface.
  • All but one vector fades away.
  • A tiny "gear" appears at the base of the normal vector, spinning counter-clockwise.
  • The normal vector and gear move to the edge of the surface, where small "teeth" appear on the boundary, and interlock with the gear.
  • The boundary begins to move along, like a conveyor belt, with the proper "induced" direction from the gear. Blue arrows appear on the boundary to show the direction of travel.
  • The normal vector and gear now move away from the edge and approach the boundary along the hole in the surface. The teeth and arrows disappear from the outside boundary.
  • Teeth now appear on the portion of the boundary along the hole.
  • Again, the gear locks into place with the boundary (now along the hole) and the "conveyor belt" begins to move in the correct direction. Note: this will be reversed from the direction on the outside boundary.
  • Red arrows appear along the boundary of the hole to show the direction traveled.
  • The gear, teeth, and normal vector all fade away and the original normal vector field returns. The arrows along all portions of the boundary reappear to indicate the orientation along the entire boundary (perhaps there could be a second hole that we ignore in the first part of the animation, and only add the direction-arrows to at the end).

Please let me know if this sounds like something you'd be willing and able to make for us. You would of course:

  1. be fully credited for the animation in our course, and
  2. have exclusive access to all of the original files (we only want the animated GIF, after it's been uploaded to Wikimedia.)

Feel free to contact me at, or my colleague at

Sincerely, Jordan

Surface orientation.gif
Done! — Kieff | KieffWikipedia | Talk 15:19, 13 August 2012 (UTC)

Surprise, surprise[edit]

A minha memória já não é que era! Afinal já conhecia o seu trabalho. Parabéns pela animação do integral de linha, é excelente! Alvesgaspar (talk) 18:25, 14 August 2012 (UTC)

Obrigado! Só não entendi o seu comentário. Tem algo matematicamente errado que preciso corrigir? — Kieff | KieffWikipedia | Talk 18:28, 14 August 2012 (UTC)
A linha vermelha é realmente a projecção de ab no plano xy? Há uma parte da animação em que não parece! Alvesgaspar (talk) 12:23, 15 August 2012 (UTC)
Sim, a linha é a projeção no plano, e a retificação da curva também está correta. — Kieff | KieffWikipedia | Talk 12:27, 15 August 2012 (UTC)
. A certa altura da animação, o ponto 'a' (a verde) aparece exactamente sobre o eixo, enquanto a sua projecção está mais acima. Logo a seguir, após uma rotação, parece haver uma translação vertical. Alvesgaspar (talk) 12:53, 15 August 2012 (UTC)
Isso é apenas artefato da projeção 3D. Não dá pra corrigir isso. Eu tentei inserir o plano ali no meio, partindo a superfície em 2, e também tentei fazer a "cortina" aparecer aos poucos, mas me pareceu excessivamente didático, visualmente complicado e a animação ficaria acima dos 12.5 megapixels, que é o limite máximo para o MediaWiki gerar miniaturas animadas. Nessas horas, eu conto com o conhecimento básico do assunto que o leitor usará para entender a animação. Uma pessoa totalmente leiga ficaria perdida. Não dá pra ser perfeito. — Kieff | KieffWikipedia | Talk 13:01, 15 August 2012 (UTC)

FP Promotion[edit]

Line integral of scalar field.gif
This image has been promoted to Featured picture!

The image File:Line integral of scalar field.gif, that you nominated on Commons:Featured picture candidates/File:Line integral of scalar field.gif has been promoted. Thank you for your contribution. If you would like to nominate another image, please do so.


/FPCBot (talk) 21:01, 21 August 2012 (UTC)

Great animation Kieff! Very helpful! Scientific29 (talk) 06:08, 28 September 2012 (UTC)

Regarding your gif work[edit]

I recently saw your graphical depiction of a line integral through a scalar field and was astonished! The power in these types of demonstrations cannot be overstated, and I would have thoroughly enjoyed these references as an undergraduate mathematics major. I'm writing to you because I feel there are lots of concepts whose comprehension would be greatly aided by visuals such as yours. I saw that you take requests, but instead I'd like to ask for advice or pointers. Where did you learn to make these animations, what software do you use, and what are some good references and tutorials on how to use it? Any extra information is immensely appreciated, as is your time and attention.

Sincerely, thank you for your response


Hey, David. Thanks for the kind words. Answering your questions:
Where did you learn to make these animations
On my own. I don't think anyone has ever written about this sort of thing. I'm just unifying whatever mathematics intuition I have with whatever artistic intuition I have. So far so good.
what software do you use
My setup is far from optimal. I actually use PHP and its built-in graphic library, GD. I have a handful of scripts that I coded to help me with some abstractions, like drawing shapes, polygons, blending of colors, 3D and 2D rotations, etc. I just generate a bunch of PNG frames and assemble into a GIF later.
You could probably do these things faster tapping some computer algebra system or some prototyping tool like Processing. I'm very used to PHP, so to me it works fine. It's also free and lightweight. But it's not meant for this.
The thing is, I like to work on this sort of thing at a low level. The graphing capabilities of most programs frustrate me, as they usually look ugly, and you can't script it to animate just how you want. Making everything from the ground up using geometric primitives lets me do anything I desire, however I want it to look, at the cost of being more time consuming.
So I don't think my setup is ideal for most people. I suggest you look into Processing, it seems really nice for this sort of thing, and you can even have it running on JavaScript and be interactive, which is the next step in this kind of illustration.
I also just recently found out about MathBox, and the author shares these principles. It's worth looking into. — Kieff | KieffWikipedia | Talk 12:43, 20 November 2012 (UTC)

File:Multiplication as scaling integers.gif[edit]

Hello Kieff

could you redo the animation with a larger dot? this dot is hard to detect so the idea of scaling is not recognised. so please make the dot larger. thanks.

Done! — Kieff | KieffWikipedia | Talk 12:18, 2 December 2012 (UTC)

Awesome work[edit]

Awesome adjective 1. inspiring awe: an awesome sight.

This definitely describes your work. In a few frames of a .gif you have condensed entire months of lectures of mathematics and physics. You really have a talent!

I second that compliment. I'm visiting your page just to say "thanks" for the simple eigenvector animation you added to wikipedia, but now I see that's kid stuff compared to the work you're capable of. Animations like that help make wikipedia a special resource, and we have people like you to thank for it. So thanks! Superbatfish (talk) 16:22, 16 December 2012 (UTC) [Washington, DC]

Qual programa[edit]

Olá, eu gostaria muito de saber qual programa ou programa você usa para fazer os gif animados... se puder responder ou me enviar email (capu3d gmail) agradeceria bastante! Obrigado. --

POV-Ray e PHP com GD, usando uma biblioteca que eu mesmo escrevi. — Kieff | KieffWikipedia | Talk 06:15, 27 December 2012 (UTC)

Your profile on Commons:Meet our illustrators[edit]

Hi Kieff,

In August, you raised a question on Commons talk:Meet our illustrators regarding adding you profile albeit you did not fully meet the number of required illustrations. You never got a reply back then, and I guess you then added your profile because noone objected in good faith.

I am sorry nobody answered you back then, but I really think you should wait until you have the required five FPs (I actually thought it was ten, when I wrote the reply). Am I correct, that now, currently, you have four featured illustrations on Commons? I have therefore removed your profile for the time being. But in case I have overlooked some FP(s), please do reinstate it, or reinstate it whenever, you get the fifth one. I am sure it will not be long.

On the sister page Commons:Meet our photographers, where 10 FPs are required, I am not familiar with anyne having mitigated the minimum requirement for inclusion. In contrast, many with more than 10 photographic FPs are not listed there. --Slaunger (talk) 17:48, 28 December 2012 (UTC)

Picture of the Year voting round 1 open[edit]

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A barnstar for you![edit]

Original Barnstar Hires.png The Original Barnstar
I present you, Sir, this original barnstar as a token of my respect. KodamPuli (talk) 09:49, 14 February 2013 (UTC)


I think the graphic File:Eigenvectors-extended.gif is misleading, because the blue arrows are not actually eigenvectors. They are actually pairs of vectors, and the identity of the vector space is the origin of the grid - hence all characterizations of vectors as arrows are supposing every arrow is drawn from the origin to the point. So, that transformation does not simply scale the vectors in the blue arrows that aren't on the central line of the stretched rectangle. So, the vectors [3,1] and [4,2] form a blue arrow in the image, but multiplying by the matrix given in en:Eigenvalues and eigenvectors#An example, you would not get a scalar multiple of either vector. LokiClock (talk) 02:53, 6 March 2013 (UTC)

Vectors aren't stuck to the origin. They're like an equivalence class: displacement and position vectors represent the same relation, but in different context. This is actually one of the main important ideas a lot of people end up forgetting, which is key to understanding how vectors don't depend on a choice of reference in physics, for instance. They end up thinking vectors "have their tail" at the origin. The beauty of vectors is precisely that they can represent a thing and relations between these things in the same package. It's a very important idea that needs to get across. Also, vectors in the animation are separated mostly in order to clearly show them. Having them all at the origin would cause a lot of overlap and confusion. — — LucasVB | LucasVBWikipedia | Talk 11:00, 6 March 2013 (UTC)
It's very important that that's not true. You're thinking of points in an affine space, not in a vector space. By definition, vector spaces have a unique identity element. LokiClock (talk) 17:12, 10 February 2014 (UTC)

Tau instead?[edit]

I was looking at File:Circle_radians.gif and wondering if you would not mind making another one, but without stopping for pi and instead stopping with tau, where tau := 2pi. Reddwarf2956 (talk) 13:20, 14 March 2013 (UTC)

I was planning on it. I will do it when I have the time (probably this weekend). — LucasVB | LucasVBWikipedia | Talk 14:04, 14 March 2013 (UTC)
Thanks. I see it done and place in Turn (geometry).


hi, Lucas, sorry. I want to know which is the program that you use to do these animations?

Hi. I address this topic on my tumblr FAQ. If you have any other questions, let me know. Cheers! — LucasVB | LucasVBWikipedia | Talk 01:54, 18 March 2013 (UTC)

Radians animated gif[edit]

I noticed your nice animated gif for the Wikipedia Radians page, and wondered how do you make such a thing?

If you can educate me a bit, maybe I could make such things too.

Hi. I address this topic on my tumblr FAQ. You'll probably be fine with something like Processing. I'm just nitpicky. Cheers! — LucasVB | LucasVBWikipedia | Talk 01:54, 18 March 2013 (UTC)

Fourier transform animated graphic[edit]

I was just reading up on recent changes to the FLAC format and digressed to your Fourier/time/frequency domains graphic ( I have to say it's fucking fantastic. Well done. — 10:51, 11 June 2013 (UTC)

Told ya so[edit]

And of course, now everyone starts to copy it from there: --Joseph Lindenberg (talk) 11:34, 28 June 2013 (UTC)

Lucas, have you considered switching the tau animation from yellow to green, like you did with the pi animation? I might be able to get it into the Pi article where tau is discussed, but only if I can shrink it to a small size. The yellow becomes unreadable when I do that now. --Joseph Lindenberg (talk) 02:19, 29 June 2013 (UTC)
I'm going to, but I haven't had the time to work on any animations recently. I should finally be able to do it later next week, once the school semester is over. — LucasVB | LucasVBWikipedia | Talk 02:42, 29 June 2013 (UTC)

small request for improvement of your "Newtons_proof_of_Keplers_second_law.gif"[edit]

Hi I am requesting that on your graphic found here: that you include an ellipse in the background for relatability. Your graphic is not helping me if I cant see the elipse for perspective and reference. The sun and planet reference was fine but then I got lost as the animation progressed. thanks

Question about one of your graphs.[edit]

Could you explain how the tan function on the trig. wikipedia page works (The graph)? I don't understand the orange line that comes up.

The tangent function's value is the length of the vertical line segment on the right of the unit circle, starting from the point (1,0) to (1,tan x). See image on the right. — LucasVB | LucasVBWikipedia | Talk 01:02, 11 November 2013 (UTC)

Would like to discuss some animations / visualisations ... please make contact[edit]

Hi Lucas.

Nice work - crisp and clear and clean !

I would like to chat to you about some animations/visualisations I am doing for a physics paper.

Your wikipedia contributions are beautiful, and clear ... and I'm hoping you might be able to assist me and give me some guidance about the images I need to produce.

I'm based in South Africa.

[email removed]

Thanks ! Rich

HiRes request[edit]

Hi Lucas,

I really enjoyed your Fourier animated gif. It captures the essence of the transform. I'm planning on using it in a lecture, to introduce the Fourier transform. I was wondering if you could make available a higher resolution version, e.g., 1024x768. Also could you make one available with a black background (or transparent background)? I'd ask for code by reading the response above, I gather the code used to generate this sequence is not easily portable at the current time.

Picture of the Year 2013 R1 Announcement[edit]

Round 1 of Picture of the Year 2013 is open![edit]

2012 Picture of the Year: A pair of European Bee-eaters in Ariège, France.

Dear Wikimedians,

Wikimedia Commons is happy to announce that the 2013 Picture of the Year competition is now open. This year will be the eighth edition of the annual Wikimedia Commons photo competition, which recognizes exceptional contributions by users on Wikimedia Commons. Wikimedia users are invited to vote for their favorite images featured on Commons during the last year (2013) to produce a single Picture of the Year.

Hundreds of images that have been rated Featured Pictures by the international Wikimedia Commons community in the past year are all entered in this competition. These images include professional animal and plant shots, breathtaking panoramas and skylines, restorations of historical images, photographs portraying the world's best architecture, impressive human portraits, and so much more.

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Scalar field 3D[edit]

What program/software did you use to render It's beautiful.

Thanks! You won't like the answer, though: it's a custom graphics library on top of GD coded in PHP (yeah yeah, but it's a long story). — LucasVB | LucasVBWikipedia | Talk 22:27, 19 April 2014 (UTC)

Pendulum 60deg.gif[edit]

Pendulum 60deg.gif

Hey LucasVB. I was just wondering exactly how you have defined your axes in this gif My guess is that it's angle and momentum (mass times velocity) but I'm not quite sure. — Inc 17:39, 9 July 2014 (UTC)

I just used angular speed (). Since the length of the pendulum and the mass are both constant, and the scale is arbitrary for the phase diagram I used, it didn't matter to use anything else. — LucasVB | LucasVBWikipedia | Talk 16:32, 9 July 2014 (UTC)

The Affine Map[edit]

That was very cool and I noted VB! Is that true?! You did that in VB? It was the one program that forced me to use Firefox so that is sort of ironic. I'm thinking of doing a website where I just start at a math point - affine maps - and see where it goes, I'm looking at a - what I think is bogus - data analytics...I mean people could use their critical thinking skills and maybe DEDUCE something instead of data analytics, but it is interesting and cool math - and cool graphs!

Fourier transform image[edit]

Hello there. This is my first time trying to edit something and I do not know if I am doing the right thing talking to the creator, so plz show mercy.

I was reading the fourier transform page and I was impressed by your animation of the red function decomposing to six individual sines. Very demonstrative.

I noticed though that when you display the frequencies of each component you assign the higher frequency to the first sine (the one with the highest amplitude) the second higher to the second sine etc.

My opinion is that this order should be reversed. The component with the higher frequency is the last (the one with the smallest amplitude) and not the first since in the same time period has the most oscillations of the six. The second higher is the 5th component etc.

Also in the text below the animation you write: "In other words, the original function can be thought of as being "amplitude given time", and the Fourier transform of the function is "amplitude given frequency"..." IMO the amplitude should not be confused with frequency. Frequency is nothing more than oscillations per second and has nothing to do with the magnitude of the pulse of a wave.

I am looking forward for your opinion on this. Regards!

Thank you for the kind words! Always good to have some feedback, too.
But I don't understand your first comment. The component wave with higher frequency (and smallest amplitude) IS last, on the right. This is exactly how it is done (on the positive frequency side, at least). The order is on ascending frequency, as it should.
And "amplitude given time" and "amplitude given frequency" do not mean I'm saying amplitude is frequency or time. It means amplitude as a function of time or frequency, which is precisely what the Fourier transform is: f(t) is amplitude for the time t, and f(w) is amplitude for the frequency w.
Are you sure you are not understanding the animation incorrectly? — LucasVB | LucasVBWikipedia | Talk

About the software you use for your artwork[edit]

Dear LucasVB

I really love your graphic works on wikipedia, as seen in

I would like to learn a bit about the software you used: may be, one day, I will able to contribute also.

Any hint is highly appreciated.

Have a great day !!


Visualization for PCA?[edit]

I just saw your visualization of the Gram-Schmidt process on reddit- very impressive. I teach remote sensing at Colorado State and would like to have something similar for PCA? Do you know of anyone who has done this? If not, would you consider making one yourself?

Thanks for your time.


Gram–Schmidt_process animation[edit]

Hello :) I was wondering what software you were using for creating animation for Gram–Schmidt_process article. If there is some guide for creating such animations I would be grateful for your insight. I've read your previous answers looks like you using PHP and some kind of graphic library. So I guess you already answered my question :)

I would like to thank you for creating such beautiful animations for Wikipedia.

Requesting gif[edit]

Hi LucasVB. I am trying to find someone who is willing to create a 3D gif like this for Level Mountain. Are you willing to help? Volcanoguy (talk) 05:21, 3 November 2015 (UTC)

Hi. The software I use is not very good for this kind of thing, as it doesn't draw "surfaces" per se. Heightmaps can be done relatively easy on POV-Ray if you have the data as image files. Do you have topographical data that is aligned with texture data? Because otherwise this would have to be arranged, which would inevitably require some GIS software or the relevant algorithms. I don't have access to those things, and it may not be trivial to do. — LucasVB | LucasVBWikipedia | Talk 07:18, 3 November 2015 (UTC)
I'm not too sure what you mean by "topographical data that is aligned with texture data". Perhaps Google Earth or NASA World Wind might be of use? Volcanoguy (talk) 06:59, 4 November 2015 (UTC)[edit]

Schön. Gefällt mir! Haste gut gemacht!

A barnstar for you![edit]

Graphic Designer Barnstar Hires.png The Graphic Designer's Barnstar
I admire your illustrations on Wikipedia and found them very useful for me to understand the illustrated concepts. Thank you! Mscdancer (talk) 17:26, 15 November 2015 (UTC)


I would like to use your image of the torus in a non fiction book on 'Rieman surfaces - Fuchsian groups' along with about 120 own figures. I am not sure whether your image is free to use in this context and/or under what conditions.

I'd appreciate your feedback. Thank you. HaGe

Hello! That image is in the public domain. You are free to use it for any purpose, even commercial ones. Cheers! — LucasVB | LucasVBWikipedia | Talk 20:09, 22 April 2016 (UTC)

Tau diagram[edit]

I don't know if you approve of tau... but I saw your lovely animation of sine and cosine, and I visited your user page and saw you welcome requests. Could you make an SVG diagram of measures of angles using tau, similar to this one from the tau website?

Oh, I just you made the nice animation of tau that's already on the page, so of course you approve of or understand tau. ^.^ — Eru·tuon 03:04, 31 August 2016 (UTC)

Looking forward to get in contact with you[edit]


I want to contact you (some mathematic-astonomic constellations),but: my English is very bad (especially when in starts in complex mathemathics terms...)

so: WHERE are you from ?

Maybe, Can we talk in GERMAN ?



— Preceding unsigned comment added by Protecta52379 (talk • contribs) 21:38, 03 January 2017 (UTC)

Thanks for responding in the Help desk![edit]

I was the one posting about software recommendations for making animated gifs, and I was stoked when you responded! You recommended drawing lines/shapes in code, and that is exactly what I am looking for! I'm going to start looking at , do you have any other tips or advice? Thanks! Popcrate (talk) 01:56, 28 February 2017 (UTC)

A barnstar for you![edit]

Graphic Designer Barnstar Hires.png The Graphic Designer's Barnstar
The animations on Fourier Series and Fourier Tranform are great! Nicoguaro (talk) 22:17, 5 April 2017 (UTC)

Reverse precession.[edit]

Is it possible to have your "Precession of a gyroscope" on the article Precession rotating in the same direction as the planet Earth does in orbit? 19:04, 14 July 2017 (UTC)

Change required in the picture[edit]

Dear LucasVB, Can you please correct File:Light dispersion conceptual waves.gif and File:Light dispersion conceptual waves.gif. If you will look at the Cauchy's equation, refractive index is inversely professional to the wavelength of incoming light. Which implies, red and yellow should be very near and blue and violet should have more widths. Means only violet should have almost 1/4 width of the total spectrum. If you wish, I can send you the exact calculations for these values.☆★Sanjeev Kumar (talk) 10:20, 14 January 2018 (UTC)

I'm sorry, but I don't think it's necessary to make such changes. I originally intended the animation to be more physically accurate regarding the dispersion, and I did include that relationship, but it didn't look good enough. I eventually dropped it for artistic license. The truth is, it was never intended to be a very accurate representation of the physics involved, because the most accurate representation is a picture, not an animation. My point in making the animations was to illustrate, conceptually (hence the file name), the relationship between color, wavelength, speed of light and a qualitative amount of dispersion. As such, I do not believe the images warrant any changes. You are free to try making a more accurate variant and replacing it, if you think it is better. — LucasVB | LucasVBWikipedia | Talk 00:54, 20 January 2018 (UTC)

Correction (?) in Dot Product in Field animation[edit]

Hello, Thank you for sharing your animations. Saves us a lot of time...

Regarding the "Line integral of vector field.gif" animation, you state that what is shown in red is a displacement vector. Shouldn't it be a velocity ?

— Preceding unsigned comment added by Dummynerd (talk • contribs) 04:50, 29 March 2018 (UTC)
You're right. It should say "velocity vector". I fixed it. Thanks! — LucasVB | LucasVBWikipedia | Talk 05:22, 29 March 2018 (UTC)

povray source[edit]

Would you be willing to let me have your povray source code for .

I'm lecturing at Oxford about Voevodsky's contribution to logic Tuesday, and I'd like to extend the animation so it shrinks the doughnut down to a circle. This would illustrate both the notion of homotopy equivalence in

homotopy theory as well as the content of Bousfield and Voevodsky's univalence theorem in topology.

— Preceding unsigned comment added by DanGrayson (talk • contribs) 16:52, 5 July 2018 (UTC)
Hello! The source code is already included in the description page, under public domain license. Look a bit lower on the page. — LucasVB | LucasVBWikipedia | Talk 16:55, 5 July 2018 (UTC)

Thanks!! DanGrayson (talk) 17:23, 5 July 2018 (UTC)